Kiaran Stapleton has been found guilty by a jury at Manchester Crown Court of murdering Indian student Anuj Bidve.
The 21-year-old, who referred to himself as 'Psycho Stapleton' at his first court appearance, admitted killing Mr Bidve, a 'random stranger', who was walking with friends through the Ordsall area of Salford in the early hours of Boxing Day last year.
Stapleton pleaded guilty to manslaughter on the grounds of diminished responsibility but denied murder.
But a jury at Manchester Crown Court found him guilty of murder and he now faces a life sentence.
Mr Bidve, 23, from Pune, western India, had come to Britain in September last year to study micro-electronics at Lancaster University and was spending Christmas with friends in Manchester.
He was on his way from his hotel walking through Ordsall to the Boxing Day sales in Manchester City Centre with a group of other Indian students when he was killed.
The trial heard how Stapleton was on the other side of the road with friend Ryan Holden when he decided to approach the group. He walked up to Mr Bidve and asked him for the time before pulling out a gun and firing a single shot into his victim's head.
Nazir Afzal, Chief Crown Prosecutor for North West Area, said Mr Bidve's murder was 'a terrible crime which shocked and appalled us all'.
'Kiaran Stapleton shot Anuj, an innocent and defenceless man, at close range without warning or provocation. Thankfully such crimes of truly random and brutal violence are extremely rare,' he said.
'It was a cowardly murder, and his reaction afterwards in trying to cover his tracks, hide from police and evade justice was also cowardly.'
Stapleton told a psychiatrist that he chose his victim because he had 'the biggest head' in his group and that instead of walking through the area he 'should have got a taxi'.
Giving evidence at the trial, Dr Adrian West told the jury that Stapleton was moving 'purposefully' towards the group of friends before Mr Bidve was shot.
Dr West, a prosecution expert, told the court Stapleton had told him: 'I blew a hole in his head, there is nothing I can say, nothing whatsoever.
'They should have got a taxi, things would have been different if they had got a taxi.'
After the shooting, Stapleton said they stashed the gun in the shed at Holden's grandmother's house before going back to his mother's in Ordsall.
He showered at his house, before dumping his clothes next to the bin at his sister's home and then went for breakfast at another friend's and saw the news on television.
After looking at the crime scene and the police activity in Ordsall Lane, Stapleton and Holden went to stay in Leigh, Wigan, with another friend where Holden suggested they douse themselves in petrol to get the gun residue off their skin.
They stayed there listening to music and 'chilling', the court heard. Stapleton said he went to bed that night and 'slept right the way through'.
'I was not thinking about what I had done,' he said. 'I was just feeling completely normal as if nothing had even happened.'
Ryan Holden later became a key prosecution witness after helping police identify Stapleton and then giving evidence against him in the trial.
The day after the murders, Kiaran Stapleton returned to the area and checked into a nearby hotel overlooking the crime scene.
CCTV images, released to Sky News, captured Stapleton coming down from his room at the Campanile Hotel for breakfast and reading a newspaper.
He was also pictured looking out of the hotel window on several occasions.
When shown the CCTV images during a police interview, he told officers: 'It's a nice picture that innit? Wouldn't mind that on a wall.'
Material recovered from his mobile phone included a photo of himself sitting smiling on a hotel bed wearing a bathrobe.
While still at large, just two days after the murder, he went to a tattoo shop in Swinton, Greater Manchester, and had a teardrop design put on his right cheek.
Prosecutor Brian Cummings QC said staff remembered the visit because the nature of the tattoo can signify that the wearer has killed someone.
In police interviews, released to Sky News, when Stapleton was asked if he had killed anyone, he joked: 'As a matter of fact, I did kill someone - my hamster.'
Stapleton showed no remorse after the murder, according to Professor Nigel Eastman, a witness for the defence.
The forensic psychiatrist told the court he was rarely made anxious by prisoners but Stapleton concerned him during interviews in his prison cell.
'I had three officers outside, I'm long in the tooth but there was just something going on I was a bit concerned at one point.'
'The defendant did not display an ability to think about emotions. I have seen no evidence of any real understanding of the emotional significance of what he's done.'
He added: 'In the criminal world, there's nothing so worrying as the nutter. Ordinary people you can cope with, you know how they react. Someone who doesn't seem normal is worrying because they are unpredictable.
'To most people it would seem just very odd to go up to someone, a stranger, and shoot them.
'I think what he's demonstrating is his very substantial lack of ability to feel what other people feel. I don't think he has any real feeling for what he's done.'
Mr Bidve's parents, Subhash and Yogini, flew from their home in Pune, India, to attend the trial and each day listened intently to the evidence from the front row of the public gallery.
As the verdict was delivered, Mrs Bidve cried and Mr Bidve bowed in his seat and later held his hands to his face.
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