On the morning of July 15 1997 the fashion designer Gianni Versace took a short walk from his oceanfront mansion to a nearby News Café.

He spent $15 on five magazines and strolled back to his $35m (£25m) mansion at 1116 Ocean Drive, South Miami Beach.

At about 8.45am, as Versace opened the mansion gates, two shots rang out. The designer fell dying onto the steps leading to his house, shot at close range in the head and neck.

Versace’s butler and the designer’s boyfriend Antonio D’Amico came running.

The killer, a rucksack on his back, wearing shorts and a baseball cap, walked calmly away.

''We were right there watching and there's nothing you can do,'' said one witness to the aftermath. ''His [Versace’s] blood was coming out like crazy. He shook a little bit and stopped moving.''

At 9.15am Versace, aged 50, was pronounced dead at the University of Miami's Jackson Memorial Hospital.

By the early afternoon, after the police tape was removed and the blood wiped off the steps, the first onlookers started laying flowers.

So began a murder mystery that for 21 years has continued to intrigue and provoke, its enduring fascination now emphatically demonstrated by the new high-budget, critically acclaimed, inevitably controversial American Crime Story series The Assassination of Gianni Versace.

To most minds, this was never a whodunit. It was, rather, a why did he do it.

The killer was tracked down within eight days, to a houseboat moored less than three miles from the Versace mansion. He had turned the pistol on himself.

A police SWAT team found the dead body of Andrew Cunanan, 27, a charming, highly intelligent male prostitute with a fondness for lying, sadomasochism and seeking out rich older men to maintain a lavish lifestyle.

Some of the more extravagant theories have sought to look beyond Cunanan, to portray him as a patsy for the mafia or even to suggest he was framed while the real murder was committed by a mob hitman.

There have been claims that Versace had links to the N’drangheta organised crime group that stretched back to when it started collecting protection money from his mother’s dress making business in Calabria, southern Italy.

As young Gianni started to prosper, the theory goes, the mob started to use his business to launder money – with, or possibly without the designer’s knowledge.

There have been reports that Versace had somehow found himself in debt to the mafia, and may even have been willing to go public about the pressure the mob was putting him under.

Some of these reports cite the testimony of two mafia men turned informers. They all make much of the strange fact that a dead dove was found beside Versace’s body. This, it was claimed, was the mafia hitman’s calling card.

But such theories have tended to attract lawsuits as well as plain indignation from the Versace family. They also seem to run up against more straightforward explanations: the police, for example, maintain that the dead dove was the victim of being hit by a stray bullet fragment in the shooting.

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To explain the Versace killing, you probably have to look no further than Andrew Cunanan.

And here you will find plenty of details but precious few absolute certainties.

Although you could probably say there was a reason why Cunanan seemed so calm as he killed Versace. By the time of that shooting, he was already a serial killer on the FBI’s Ten Most Wanted list.

His spree had begun on Sunday April 27 1997, some 1,790 miles from Miami, in Minneapolis.

The first victim to be found was Jeffrey Trail, 28, a former US Navy lieutenant who had become friends with Cunanan while they were both living in San Diego, California.

Cunanan had come to see Mr Trail as his best friend, his “brother”. Mr Trail came to see Cunanan as an encumbrance.

Maureen Orth, the Vanity Fair writer whose book formed some of the inspiration for The Assassination of Gianni Versace, wrote of Mr Trail’s exasperation at being placed in the false, name-dropping, self-aggrandising stories that Cunanan loved to tell his friends.

In late 1996, Ms Orth was told, there had been a big falling out. Mr Trail told friends he never wanted to see Cunanan again.

But, Ms Orth was also told, “he [Cunanan] was like a relative you didn’t like... you had to let him stay.”

And on Friday 25 April 1997 Cunanan flew from San Francisco to Minneapolis airport, where he was picked up by Mr Trail’s friend David Madson.

Mr Madson, 33, a talented architect, was more than just Cunanan’s former lover from the time they met in San Francisco in 1995. He was, according to Ms Orth, “the great unrequited love of Cunanan’s life.”

They had broken up in the spring of 1996, but Cunanan still kept Mr Madson’s picture taped to his fridge door.

Mr Madson, for his part, was uneasy about his ex-boyfriend’s visit. He had split from him fearing he might be into something “shady”, possibly international drug smuggling.

In fact, the source of the kind of easy money that allowed Cunanan to pay for his friends’ dinner and add a $200 tip for the waiter appears to have been wealthy gay men. But according to some reports, Mr Madson was right to be worried.

A week before he arrived in Minneapolis, Orth recounted, Cunanan met his friend John Semerau in a gay bar. He told him of an S&M party he was going to, and then quarrelled with him, violently.

“He grabbed me around the neck so hard he was choking me by his grip,” Mr Semerau recalled, “Now I realise the guy was hunting, getting the thrill of the hunt, the thrill of the kill. Something had snapped in him.”

And this was the ex-friend that Jeffrey Trail encountered in Mr Madson’s loft apartment.

On Sunday night a neighbour reported hearing someone yell "Get the fuck out" followed by several thuds that lasted for some 30 seconds.

On Tuesday afternoon, the superintendent of the block entered the apartment to find blood spattered all over the door and two sets of bloody footprints. Mr Trail’s body had been rolled up inside a carpet. He had been hit from behind and battered to death with the clawhammer that was found, bloodstained, beside the body.

Police also found an empty holster for a .40 calibre pistol and an ammunition box that was missing ten bullets. And by this time Mr Madson hadn’t turned up for work for two days running.

His body was found on Saturday 3 May in tall grass beside Rush Lake, 50 miles from Minneapolis. He had been shot three times. A .40 calibre bullet was found in his chest.

But by now Cunanan was in Chicago. He had taken Mr Madson’s Jeep Cherokee and driven to the elegant lakefront home of 72-year-old Lee Miglin, a much-respected real estate multimillionaire, married with two grown-up children.

And here Cunanan committed a murder of almost unbelievable savagery.

Attacking Mr Miglin in his garage, he wrapped his head in duct tape, but left airholes open at the nose.

He repeatedly punctured his victim’s chest with a pair of pruning shears before almost cutting his head clean off with a bow saw. Then he got into Mr Miglin’s Lexus car and repeatedly drove it back and forth over the body.

The killer calmly let himself into the house, ate a sandwich in the library and shaved in the white-marble bedroom, before driving away in Mr Miglin’s green 1994 Lexus with a load of cash.

On 9 May Cunanan came to Finn’s Point Civil War Cemetery in Pennsville, New Jersey.

There he forced the 45-year-old caretaker William Reese to go to the basement of the cemetery lodge before shooting him in the back of the head with the pistol he had already used to kill Mr Madson and would soon use to murder Versace.

It seems that to Cunanan, Mr Reese, the father of a 12-year-old son, the husband of a primary school librarian, was just a “functional homicide,” murdered for his red Chevrolet pickup truck, the vehicle that would take the serial killer to the gates of the Versace mansion.

The biggest questions seem to lie behind the motives for killing Miglin and Versace.

At first Chicago police were convinced that there had to be a link between Miglin and Cunanan. But they struggled to find one, and came to lean towards a “stranger danger” theory. Perhaps Miglin, too, had been murdered just so Cunanan, the wanted fugitive, could switch vehicles.

In 2014, however, ABC 7 Chicago acquired FBI files that suggested something rather different. In the files were reports that Miglin and Cunanan had been friends, of the kind who would pick up a local rent boy for sex.

To some, the circumstantial evidence makes the theory of a gay sexual link seem even more appealing.

Apart from the important caveat that he had a family, Miglin fitted the profile of the kind of wealthy man that Cunanan liked to go for.

“Andrew did his homework,” one San Diego acquaintance was quoted as saying. “He would investigate older, wealthy gay men who didn’t have families, and he would place himself in those circles. And that was his living.”

Cunanan was known to visit Chicago frequently. And, Orth reported, Cunanan had kept a 1988 copy of Architectural Digest which featured the home of Miglin’s partner, Paul Beitler.

Miglin’s family has always insisted there was no link at all. The multimillionaire’s son Duke told ABC 7 Chicago that the Police had come to the conclusion that the FBI had been misinformed.

And in July 1997 Chicago police superintendent Matt Rodriguez had been emphatic.

"I can tell you unequivocally,” he stated, “That we have not found a link between Andrew Cunanan and anyone in the Miglin family.”

There are similar bitter, irreconcilable differences when it comes to the links that Cunanan may or may not have had with Versace.

Gianni Versace

Ms Orth says Cunanan and Versace had met in 1990, in the VIP room of the San Francisco nightclub Colossus.

According to her account the designer had noticed Cunanan, walked over to him and thrilled the younger man by striking up a brief conversation with the line “I know you, Lago di Como [Versace’s Lake Como residence], no?”

Ms Orth said another witness recalled seeing Cunanan with Versace in a chauffeur-driven car in the autumn of 1990.

She has insisted: “There is no doubt in my mind that those two met. That all is absolutely fact-based, on-the-record reporting.”

The Versace family is equally adamant that Versace and Cunanan never met, as its statement in relation to the American Crime Story series make clear.

“The Orth book itself is full of gossip and speculation,” it reads. “Orth never received any information from the Versace family. She has no basis to make claims about the intimate personal life of Gianni Versace or other family members.”

The vehemence of the statement can perhaps be explained by the dark shadow cast over the Versace story by HIV.

In late July 1997 Time Magazine quoted a San Diego Aids counsellor as saying he had been visited by Cunanan in late 1996.

This was at a time before the most advanced antiretroviral drugs, when HIV was seen as effectively a death sentence.

And Cunanan was reported to have asked about Aids before blurting out: "If I find out who did this to me, I'm gonna get them!"

Then in 2014 the FBI file was alleged to have shown that Cunanan had told friends: "If I had AIDS or if someone did that to me I would go on a five-state killing spree and take everyone with me I could.”

In August 1997 it was reported that tests performed on Cunanan’s body showed that he was, in fact, HIV negative.

Yet some have continued to speculate that, worried he might have HIV, Cunanan was out to kill those with whom he had had unprotected sex.

Which makes Orth’s contention that Versace was HIV positive about as incendiary as it is possible to get.

"I was told on the record by the lead detective on Miami Beach that he had heard from the medical examiner who did the blood work that he was [HIV-positive]," she has said.

And the Versace family have hit back with the strongest of denials.

The statement reads: "Orth makes assertions about Gianni Versace’s medical condition based on a person who claims he reviewed a post-mortem test result, but she admits it would have been illegal for the person to have reviewed the report in the first place (if it existed at all).

“In making her lurid claims, she ignores contrary information provided by members of Mr. Versace’s family, who were in the best position to know the facts of his life. It is sad and reprehensible that the producers [of The Assassination of Gianni Versace] have chosen to present the distorted and bogus version created by Maureen Orth."

You get the sense that the Versace family are entirely behind Mr D'Amico, the designer's boyfriend of 15 years, who told the Observer before the TV series aired in America: “Unfortunately Gianni died, unfortunately this guy killed him, but now, let it drop.”

You also get the disturbing sense that the killer himself would have been delighted that people weren't letting it drop.

This, as Ms Orth has pointed out, was the man who could describe the texture and delicacy of the blowfish he said he had eaten at an $850 Japanese lunch – but who may have been fantasising.

And even if he really had eaten the potentially poisonous delicacy, Cunanan knew the rich man’s life of his carefully targeted sugar daddies would never truly be his.

But it was Versace’s, and so was the fame.

The American Crime Story voiceover has actor Darren Criss, as Cunanan, intoning: “This world has wasted me and yet this world also made you, Mr. Versace, into a star. You’re not better than me or the same. The only difference is you got lucky."

Perhaps, after all, that is where the motive lies, if not for the other murders, then at least for the assassination of Gianni Versace.

In his San Diego high school yearbook, they described Cunanan as the pupil “most likely to be remembered”.

And maybe the 18-year-old Cunanan already sensed the beginnings of a fatal hankering for notoriety.