The morning Young Thug is due to play his first headline show in London, another American rapper is making headlines. Tyler, the Creator has been banned from the UK by home secretary Theresa May, apparently because he “made statements that may foster hatred, which might lead to intercommunity violence in the UK”.

Meanwhile, Young Thug was gliding across the border on the Eurostar from Paris, without so much as a pat-down. Whereas Tyler is a geeky rapper who has never been charged with a serious crime in his life, Young Thug had his home raided in July after he allegedly threatened to kill a mall security guard in Georgia. During the raid, police found guns, cocaine and marijuana and he was hit with three counts of felony arms possession. That all happened on the same day an indictment was issued claiming that Thug, along with his label boss at Cash Money Records, Birdman, conspired to have Thug’s hero and mentor Lil Wayne murdered (a charge he strenuously denies).

All of that might create the picture of a typical gangster-turned-rapper but, in fact, nothing about Thug (which is apparently what even his closest friends call him) is typical. He is one of the most interesting characters in hip-hop today, seemingly drunk on his own eccentricity. He doesn’t pretend to have left gang life behind – on his outro to a Dej Loaf track released last year he snarks, “As a matter of fact, I’m one of the biggest Bloods in fucking America” – but these days he is probably better known for his gender-fluidity, recently photographed in a tutu, a lace floral Gucci top and a leopard-print dress. Rumours about his sexuality abound, but Thug says he is neither gay nor straight.

You might expect this seeming disjunction to influence his music, but his lyrics rarely ponder the realities of his complex existence, instead portraying a bombastic and often surreal version of his life. His latest mixtape, Slime Season, presents an almost sci-fi version of rap excess. He talks about his own beauty (“I’m a fuckin’ stunna, ass big, Hummer”) and outlandish personality (“I’m an earthling in disguise”) in a way no other rapper would. His surrealist imagery is compounded by his music videos, which combine hip-hop cliches with Lynchian dream sequences – his recent video for Best Friend features Thug walking in on himself making out with his female alter ego, before his ghost sits down to a breakfast cereal dinner party.

The plan today is to catch Thug for a few hours before his London debut to get a sense of the man. “It might not be a traditional interview,” warns his publicist. I sense she has had a few issues in the past. He missed two photoshoots for a Complex magazine cover last year, eventually showing up at the third and answering six questions with two-word answers: “The quickest interview in history,” according to the writer. In a Dazed & Confused interview earlier this year, the writer said: “Each time he speaks more than five words, it feels like an astounding gift from the universe.”

We get to the venue, and I’m told Thug will be there in about 30 minutes. I am told this every 30 minutes for the next five hours. Eventually it’s agreed that we’ll have to wait until after the show – which is explosively energetic and musically ramshackle, Thug mostly shouting over the full versions of his own songs, with the vocals still turned up – and then at around 11.30pm, I am shown into the dressing room.

It’s hardly the intimate setting you’d want. He’s joined on the sofa by his new fiance, his sister who is also his manager and a few other members of his entourage. He’s handed a cup of purple medicinal liquid in a polystyrene cup which is known in the hip-hop world as “lean”, a powerful codeine-based cocktail that is supposed to make you lethargic and slurry. I worry he might be monosyllabic, but he seems in a good mood. “This is one of the first tours I did where I wasn’t rushing to go home,” he says. Does he enjoy it more than playing in the US? “Europe is a trillion times tighter than the US. These shows make me stop smoking. You can’t fucking play. You gotta stop, you can’t do drugs, I’ve been slacking drugs,” he says, lean still in hand.

Hits bring money, money bring power, power bring fame, fame change the game Young Thug

Young Thug performs at Boston’s House of Blues. Photograph: Henrique Plantikow for the Guardian

One of the things I’m surprised about, I tell him, is how relaxed he always seems. Despite his work rate – since 2011, he has released 12 full-length mixtapes, as well as working on his debut album, Hy!£UN35 (yes, that really is its title), to be released later this year. He tells me he makes “at least five to 10 songs a week”. At the same time, he’s touring, getting married, getting arrested – yet he never seems edgy. Is there nothing that plays on his mind? What’s the first thing he thinks about when he wakes up in the morning?

“Whatever I think of, that’s what I do. I wake up and think, ‘I want to buy a car’, I buy a car. I wake up and be like, ‘I just want to lay in bed with my girl’, I do that. I wake up and want to rap, I rap. So whatever I think of. But really, I be on the money.” He turns to me. “We need money. We need hits. Hits bring money, money bring power, power bring fame, fame change the game. You know what I’m saying?”

“You’re saying that you’re a very impulsive person.”

“Impulsive? Are you kidding,” interrupts his fiancee. “He’ll be like: ‘Meet me at the car lot.’ I say: ‘What car lot? It’s 7am!’ and he’ll say: ‘I’m at the BMW car lot.’ I don’t even know where it is or how he got there. Or he’ll be like: ‘Let’s go to Paris tomorrow. Go on, make it happen,’ and then hang up. He won’t even wait for a response. So then we’re going to Paris. He’s super spontaneous.”

It’s only recently that Thug has had the wealth and freedom to live a life of impetuosity. One of 11 children, he spent much of his adolescence in juvenile detention, after breaking his middle-school teacher’s arm. When he left the programme, he started recording, mostly in a wardrobe in a friend’s bedroom. In 2011, he began releasing his first mixtape series, I Came From Nothing. You start to get a sense of Young Thug on those early tapes – his sing-song style, his cartoonish imagery (“I’ll eat your ass up – then burp”). But it’s a long way from the Thug of today.

“I didn’t used to do shows because I used to be so shy. We’d perform and I’d be at the back, thinking of another song. I was so shy, I ain’t never getting in front of the camera, I would never get on stage. I was too shy, boy.”

What changed?

He sniggers. “The bankroll.”

I wonder if that’s just the easy response, or whether there’s more than money that motivates him. Thug thinks about that. “I don’t ever want to be like a peasant. I want to always be all right. But motivation is fans – not your kids, your mum, none of that. All of that matters, but number one is your fans. To me, it’s more about music – so I don’t really care about that. I could live in a condo.” He stops and then cricks his head. “It’s gotta be a nice condo though.”

When he was still unsigned, he gave an interview to a small YouTube channel in which he said he believed he would one day sign to Cash Money and work with Lil Wayne. A few years later, both Lil Wayne and Gucci Mane, another of Thug’s heroes, tried to claim him as a protege, with Gucci signing him to his record label and Wayne acting as a mentor. But it was the support of Birdman, the owner of Cash Money and one of the most powerful people in hip-hop, that has led many to believe Thug is being anointed as the genre’s next huge star. When Birdman included Young Thug in his Rich Gang supergroup, it seemed as though he was creating a sequel to Lil Wayne’s Young Money label, which launched Nicki Minaj and Drake.

What happened next is complicated. The short version is that Lil Wayne’s relationship with Birdman deteriorated while Thug’s relationship with Birdman became stronger than ever. Thug still admired Wayne and wanted to name his mixtape Tha Carter V, in tribute to his hero’s most famous series of albums. Wayne wouldn’t allow it, so the name was changed to Barter 6 (because Bloods put the letter “B” in front of words beginning with C). That seemed like the end of the relationship with his idol.

Then, in July, both Young Thug and Birdman were named by Georgia prosecutors in a case against Thug’s tour manager, Jimmy “Peewee” Winfrey, who was charged with a shooting at Wayne’s tour bus in April. In the indictment, it said that Winfrey had called Thug before the shooting and Birdman after, as well claiming Thug had threatened Wayne in his music and videos.

It’s all about the music – I could live in a condo. It’s gotta be a nice condo though Young Thug

Young Thug and Cash Money label boss, Birdman in New York. Photograph: Bennett Raglin/BET/Getty Images

Hours before I arrive for the interview, I received an email from Thug’s publicist telling me to refrain from asking about “Lil Wayne, Birdman or any ongoing legal cases,” and this was a condition for the interview taking place. So instead, we talk generally about the role of mentors in Thug’s career. What did it mean to have Gucci Mane and Birdman present him as their prodigy?

“It comes with growth. Sometimes people grow too fast when they sell, they won’t look at it as what it is. I always look at it as what it is. It don’t matter how big you is – motherfucker, this is Birdman, he has half a billion dollars. He call, you need to answer the phone. It’s like, I’m just human. If Gucci calling your phone – the man’s a fucking legend – why won’t you answer your phone? How could you ever think you’re bigger than him?”

Whatever the realities of these fractured relationships, in the space of such a short time, he’s gone from the mentee to the posterboy, his global stardom threatening to eclipse his heroes. Beyond the Atlanta hip-hop scene, he’s appeared on club bangers such as Juicy J and Nicki Minaj’s Low, and even Jamie xx’s In Colour album, where Thug’s sing-song rap style is put to spectacular use on the dancehall-inflected I Know There’s Gonna Be (Good Times). Kanye told Thug he’s “like Bob Marley” and is desperate to make an album with the younger rapper. Does he even recognise the connection between his old career and his new one?

“I mean, we still do it the same way, but it’s less gangster, you know what I’m saying? More white motherfuckers and important motherfuckers. There’s less gangsters, less drugs. I have a girlfriend now, so no girls. I think all of those things make me more of an artist, though. If I didn’t have a girlfriend, I’d have 10 girls at the studio and they would make me not rap. I’d be chilling and getting stoned. It’s like, boom! – I’ve got a girlfriend. It turned out to be a good thing because it made me a rapper.”

As his career has become more professional, so his style has become more wild. In his first TV performance, he wore brown leather trousers with a pink flag flying out the back, an effeminate take on his gang roots. Since then, his dressing-up box has become more and more varied, and during New York Fashion week in September, he starred in a Vogue video alongside a string of supermodels who danced to Good Times. It’s become a huge talking point, and he’s been subjected to homophobic comments on social media.

“I like everything that people say,” he insists. “No matter what they say. You gay, you a punk. You got a nice girlfriend, you’re ugly, you can’t rap, you’re the hardest.” Is it important that hip-hop has looks other than the hyper-masculine stereotype? His manager jumps in: “That’s why you like him in Europe. That’s how you dress. If he was some masculine guy, I’m not saying they wouldn’t like him, but he’s more relatable. To people who just like old hip-hop.”

“Yeah,” agrees Thug, “Because you’re from Atlanta, Georgia, and you’re dressed like a fucking European. Of course.”

It’s interesting to hear what the big egos of hip-hop say when they’re asked to talk about themselves. Drake is all charm and schmoozing, deflecting questions away with a gag whenever he can. Kanye overheats with his efforts to push the envelope. But Thug seems unable to restrict himself with a gameplan: his music and image thrive on impulsivity. So you’re never going to get a sober analysis of his own place in the world – how could he tell you what the future holds when tomorrow he could sack everything off and go to Paris?

Instead, the best you’re going to get is a quick glimpse of the mania as it happens. There is a sense in which Young Thug’s main line of business is to confound expectations around rap, sexuality, criminality and art. If that’s his business, then he has become an impresario, using his music and wealth to push the limits of what a rapper can be. After all: hits bring money, money bring power, power bring fame, fame change the game.