Johnny Depp is still wearing his pirate teeth - gold and platinum and twinkling - and they look like they belong. In many ways he was always a pirate - of hearts and souls at least. He is a one-man subculture, a fairy tale you grew up with. I have met him several times now. The more I know him, the more I like him - but the more he seems to both contradict and confirm all the myths about him.

Did he fill the bath with champagne when he was with Kate Moss and have the barman come up and make some cocktails? No, but he would like to have done. Did he chase the paparazzi in a most threatening manner when they tried to snap Vanessa Paradis's baby tummy? Of course he did - anything to protect his girl.

Is it true that this edgy, dark, outsider actor, famed for playing losers, drug addicts, transvestites and various gothically lost souls in indie movies, is now a blockbuster superhero - or at least a super antihero? The first film in the Pirates of the Caribbean trilogy took $650m (£358m) at the box office and Depp's Captain Jack was nominated for Oscar gold. It seems altogether a myth of reinvention - but it's true.

For the Los Angeles premiere of Dead Man's Chest, there was a red carpet three miles long. Producer Jerry Bruckheimer, who only ever intends to make blockbusters, says that the trilogy simply couldn't have happened without Depp. Bill Nighy, who rather surreally plays a giant squid pirate, says: "Johnny's Jack Sparrow is one of those rare performances that has entered the language. It will survive down the years and I can risk describing it as iconic."

That's quite a turnaround because at the onset of the first movie Depp was considered too edgy for Disney. That is not to say that the man in front of me has gone soft. He is still a pirate, going his own way, living by his own rules, which includes cancelling all his one-on-one international interviews except for me. Now do you see why I love him? Maybe this is because Johnny would never let down anybody that he actually knew. Or maybe it was because the last time we met, I gave him a dildo named Johnny. There was a reason: he had just done The Libertine, playing the sexually omnivorous Earl of Rochester. "It was a gorgeous gift" he says smiling naughtily. "A great gift."

People just want to give things to Johnny, except, of course, Disney, who didn't want to give him the part of Jack in the beginning. "I took a lot of heat from Disney and the people that write the cheques, but I really did feel strongly that I was heading in the right direction," he says. "This was my take on Captain Jack. This was who I thought he should be."

Jack Sparrow is both a pirate hero and a pirate villain. He appeals to little kids and hardened adults in equal measure. He is charmless and charming, the perfect antidote of louche sexiness against the uptight Will Turner, played by Orlando Bloom. Originally he said he based the character on a mixture of Pepé Le Pew, the Looney Tunes cartoon skunk, and Rolling Stone Keith Richards, whom he cajoled out of illness to play a pirate relative in the final Pirates film. Is he going to be his dad? "Something like that," Depp says coyly. "He has to be a relative - there's no way around that. We did get together in a hotel room and dress up as pirates. He looked beautiful in the clothes and his hair was in dreads. Gorgeous! Just gorgeous!" He laughs and twinkles.

Despite the "heavy amount of salesmanship involved", there are aspects of being a pirate that Johnny truly loves. He is wearing a grey fedora, tousled hair and soulful eyes. They don't miss anything and they reveal everything. He has got a collection of bracelets, one made by his daughter, Lily Rose, another a cross wound round with drawings by his son, Jack. He has Jack's name tattooed on his arm and just above it, Jack Sparrow's pirate crest. Jack the son came before Jack the pirate.

There is also the famous Wino Forever tattoo, which used to be the famous Winona Forever tattoo. His love affair with a good Bordeaux outlasted his relationship with the actor.

It is more than 20 years since Depp quit as the cutesy cop in the American television series 21 Jump Street, saying he didn't want to be a novelty boy "stapled to a box of cereal on a one-way collision course bound for the lunch box. A franchise boy, fucked and plucked with no escape." And now, after What's Eating Gilbert Grape, Edward Scissorhands, Ed Wood, Finding Neverland, Corpse Bride etc, I am the proud owner of a Captain Jack Sparrow doll with detachable bottle of rum. "Do you have the one that talks?" he asks excitedly. "The one that talks speaks lines from the movie - but they didn't ask me to do it. I don't quite understand why. He speaks like me but is not me."

Now people thinking of him as a product doesn't bother him because he knows he's not one. He doesn't even see his own story as an arc of struggle, success, failure, triumph. "I was in a cluster of movies that by Hollywood definitions were not successful. They were flops. I was considered box-office poison but to me they were all successful and I don't feel any different about a success or failure. I don't know how to explain it, but by some miracle I have always been able to choose my characters for movies. Being able to get jobs throughout the 90s when, in the language of Hollywood, I was box-office poison should have been hard, yet I was able to do every single film I wanted to do and with every film-maker I wanted to work with. To me, whether I'm playing Ed Wood or Fear and Loathing, all these movies have commercial potential. Pirates could have easily flopped. It's always a crap shoot."

For most of the 90s he was, by his own definition, "who I was before I became me". For the most part he pursued dark characters in movies and dark love. Or at least wrong love. There were relationships with actors Sherilyn Fenn, Jennifer Grey and Winona Ryder, plus, most mythically, Kate Moss. "I felt weirdness for many years. I went through periods where I wasted time and felt awful about stuff. Just not comfortable in my own skin."

Drugs for him were never recreational; they were to anaesthetise. The seismic shift came not when his friend River Phoenix died of an overdose outside the club that Depp part-owned, the Viper Room in West Hollywood, but with the birth of his daughter, Lily Rose. Coming from anyone else, this would seem contrived, ridiculous, pretentious. Coming from him, it seems a simple fact. "It was not just the greatest thing that ever happened," he says. "It's the only thing that ever happened to me. I helped give our daughter life and she gave me life." Lily Rose is now seven and Jack is four. There's very much a sense that Vanessa Paradis was not just the right woman, but she came at the right time. He was ready for children and she became pregnant three months after they met. "You have this feeling . . . I can't really explain it but I had it when I saw Vanessa. I first saw her across a room, just her back, and it was an instant thought of, oh my God, what's happening? But even then I had no way of knowing how great a person she was and how great a mother she would be."

I read a rumour that he wanted to take a step back from movie-making so that Paradis could work more. "There is some truth in that, although they aren't going to let me take a break soon. I won't get much time off for the next couple of years."

He has coaxed Bruce Robinson, of Withnail And I fame, to direct The Rum Diary, based on a Hunter S Thompson book, and he is producing and starring in Shantaram, an adaptation of Gregory David Roberts' novel about an Australian heroin addict who escapes prison and becomes a doctor in the slums of India. Is he worried that Vanessa working will change the dynamic of their relationship? "No," he says, mystified. "If she wants to work, she certainly can. She's been working on her album and I think she'll tour with that. As far as movies are concerned, nothing's come up that she's interested in. When we first got together, she was on tour and I was 'tour daddy' on the road. For a lot of time it was just me and my daughter. We've always been very good about being able to control distance and separation. When I was doing Pirates in Dominica, I didn't bring them to the location because it was a pain in the ass - three planes - for them to get there. But you get to the point where you've been working away for three weeks and you're just trying to maintain yourself until you see them again. It was tough, really tough, and I wouldn't do it for more than three weeks."

Although he says this very gently you know it's something he would be unmoveable on. He's grounded in his family, not his work, and must relish his present stability. He was born in Kentuck and grew up in Florida, where his parents - mother a waitress, father a civil engineer - split up when he was 15. "I was pretty much ready to leave myself, and did so not long after that. They had had a prickly relationship for a number of years, so on the one hand it was a relief. On the other it was a radical change for my mum and she got very ill. So there was never any time for that kid to feel bad about the parents splitting up because the kid in me had to go straight to the mom to look after her to make sure she was OK. There was never time for the mourning of the loss of family."

Perhaps he did his mourning subconsciously. Perhaps that's what he means when he says "I was revealed to myself" when he found himself in a family again.

Here's the contradiction: Johnny Depp seems straightforward but you know he's complex. "Well," he says, "I was given the 'weird' badge but I think everybody's weird and that's the key to it. We should celebrate our individuality, not be embarrassed or ashamed of it. We all have idiosyncrasies, tics that are obsessive-compulsive. People do themselves a great disservice by not allowing themselves to see who they really are because they are afraid."

Maybe that's why we all love Johnny - because we're all weird and he lets us embrace it. It seems pretty weird that in the meantime we cannot be sure about the urban myths of things that have happened and things that are supposed to have happened. For instance, I read that he was going to play Michael Hutchence in a movie. "I have read that and it's not true," he says. "Michael was a beautiful person and an interesting guy. He spoke fluent Chinese. He was the 007 of rock'n'roll. I'd like him to be remembered in a different way than that INXS TV show where they auditioned to replace him."

I also read that Kate Moss was going to play opposite him as Paula Yates, I tell him. He falls back in his chair. First his eyes are frozen in shock and then he laughs. "That's a stretch! Paula was so different from Kate physically and in every other way. Wow, somebody really went for it when they wrote that story."

He jumps up and frisks the room for an ashtray; he needs to roll a liquorice-paper cigarette to calm him after that one. The mention of Kate charges the room a little. He sends his support and his love for her from afar.

"She's a great girl. She's got a great brain on her. I sent out signals of support to the best of my ability to express the shock of the treatment she got by the press dragging her through the mud like that," he told me last time we met. He predicted that she would come back stronger than ever. He knows her in a deep way but not in a day-to-day way any more. "I was not good for Kate," he once told me with a lingering sadness. One suspects, though, that that is not why they are no longer in touch. He is hugely loyal, hugely old-fashioned, and I think he just wants to be involved with Vanessa, so much so that even a screen kiss with Keira Knightley for Dead Man's Chest got him twitchy and feeling a little awkward.

Another rumour I had read was that he wanted to move to London, next door to Liam Gallagher. "Ten or 12 years ago that might have been true. No disrespect to Liam, but I don't think he's the guy I want for my neighbour and I guarantee he wouldn't want me. I like London but if I lived there - for an outsider like me it would lose the magic."

Does he still think of himself as an outsider? "I meant 'foreigner', but I don't think I ever felt like an outsider in the way you mean. I just never felt like an insider. And I was never really interested in being one."

You mean you don't want to throw televisions out of the window any more? "Well, as I said, having kids changed that a lot. It revealed a lot. But I still have that stuff in me, the hillbilly rage as it's been called. I may even break a television set here and there; it just doesn't get written about because I'm not doing it in a hotel. I basically wrote off all spirits because they get me into trouble, although a good bottle of rum can be pretty spectacular. But there are endless files in the human body that I can access. The hillbilly rage is somewhere in there - it's genetic, it's part of your conditioning and your upbringing. Playing these kind of characters in films just gives me the opportunity to relieve myself of this kind of stuff. Captain Jack does that for me in a weird kind of way. Its given me the key to fun."

So for now, Johnny Depp is ready to look elegantly wrecked, sashaying into a further pirate adventure before he hangs up Captain Jack's cutlass forever. We hug goodbye and it's a warm and proper hug where I tell him he's lovely and he squeezes me tighter.

Outside, hundreds of the world's foreign press are gathered waiting to kill me because of what went on between me and Johnny in the hotel room. Later again, sitting in the hotel cafe on Wilshire Boulevard, blood-curdling screams suddenly rip into the evening air: "JOHNNY! JOHNNY! JOHNNY!" Some kids have found out that he is inside the hotel. They're flailing their arms, legs, everything, just like the thousands who turned up the day before at the premiere, none of whom Johnny wanted to disappoint. He signed everything, greeted every fan and had to be dragged into the movie. He won't be allowed to let go of Captain Jack quite yet. Maybe he never will.