Detectives publicly identified Mr Wallace and launched a murder inquiry, involving 60 officers, into the killing. Mr Wallace, 18, a Tesco shelf stacker, disappeared a fortnight ago after a works night out at a local hotel in Kilmarnock, less than 10 miles from Barrassie beach near Troon, where his head was found on Wednesday.
Police are bemused by the killing - they say there is no apparent motive. They described him as "a popular, well-respected young man, who was keen on snooker and golf and loved music". He was single and lived with his parents and his older brother, Colin, 21. A police statement added: "There seems to be no reason why something so awful should have happened to him."
Detectives have not ruled out a gangland killing, but the circumstances surrounding the recovery of the body parts suggests that the killer may be playing a bizarre game.
The arms and legs were dumped in black bin bags in Loch Lomond at a favourite spot for training police divers, who chanced upon the first body parts while on an exercise on 6 December, the day after Mr Wallace's disappearance. His head was then found above the high-water mark on Barrassie beach on Wednesday by a woman walking her dog in an area popular with day trippers suggesting that the killer expected it to be found.
Dr James Mann, a retired doctor who examined the head, said that the victim appeared to have died only a short time before. He said: "From my experience he had not been dead long. If that had been the case there would have been some decomposition, but there was not. It was not bloated and the fact it was found so far above the high-tide mark doesn't point to it being washed up."
Yet the dead man's limbs had been found nearly 10 days earlier, indicating that the head may have been kept in cold storage after Mr Wallace died. The police said that, since the remains were found so far apart, they are convinced that a vehicle must have been used to take them to the disposal site.
Mr Wallace was last seen by a friend at about 1.45am on Sunday 5 December in Kilmarnock town centre, heading towards a nightclub. and he is believed to have told friends that he was on his way to a party in a nearby village. He last spoke to his father, Ian, 49, three hours earlier, his final words being, "See you tomorrow, Dad."
The area in Kilmarnock where he was last seen is extensively covered by CCTV cameras, which police are examining for clues. Mr Wallace, who was 6ft 2ins tall with brown hair and off medium build, was wearing a cream-coloured jacket, light blue shirt and jeans.
Detective Superintendent Geates, who is leading the investigation, said: "Without doubt this a horrifying murder that has stunned the whole community and shocked experienced detectives. As you can imagine the family's sense of shock and grief at losing their son in such appalling circumstances is unbearable."Reuse content