But Tihi denies having any murderous intent, the court heard.
Whether there was murderous intent is a "very important issue generally" in the trial but particularly for Tihi, Mr Shamy said. Mr Shamy said murderous intent must be present when the act is committed, not before or after.
Crown prosecutor Deidre Orchard told the High Court in Christchurch that the trio had planned to administer a serious beating.
They were seen on CCTV "loitering" near Parata's cell during recreation time that morning, the Crown alleges.
When Parata walked back into his cell at 9.22am, Tihi is alleged to have walked behind him, his hands bound in white tape.
He's followed by Reuben who the Crown says "launched himself" into the cell.
Betham, the Crown alleges, stood outside Parata's cell and is then seen on CCTV entering the cell and closing the door behind him.
Six seconds later, Betham is alleged to emerge from cell, followed by Tihi and then Reuben.
In a "little less than 90 seconds", Parata is battered around the head so badly that he later died in hospital, the Crown says.
Parata was found lying on his bed at the end of recreation time by a prison officer at 9.50am - almost half an hour later, the court heard.
The guard noticed that Parata's cell was messy, which was out of character for the "house-proud" inmate. He also saw bloodied paper in the toilet and blood on a wall.
Realising that Parata had been assaulted, he closed the cell door, locked it, and went to get help.
But the first prison medical officer didn't get to the cell until 10.23am.
She found Parata's eyes fully swollen and shut tight. He was sweating heavily and there was minimal response to verbal commands, the court heard.
"She very quickly found his condition to be serious," Ms Orchard said.
He was rushed to Christchurch Hospital by ambulance with serious facial injuries, low blood pressure, and showing clear symptoms of brain injury, including muscle spasms, and jaw clamps.
Emergency surgery couldn't reverse his brain damage and he died five days later, the court heard.
Pathologist Dr Martin Sage found that Parata had suffered extensive blunt force injuries to his head, face and neck.
He identified seven forceful head impacts but concluded that it was "almost certainly an underestimate", Ms Orchard told the jury.
Dr Sage will later tell the court that Parata could have been stomped on the back of his head, propelling his head into the cell floor.
The three defendants were soon identified as suspects.
But by the time police showed up about five hours later, the Crown alleges, they'd had "ample opportunity to clean up".
Ms Orchard claims that their clothes had been washed and were still wet.
There was no evidence of Parata's blood in either their cells or on their clothes, the court heard.
The house-proud Parata had also "corrupted" the assault scene himself after he'd tried to clean up much of the blood.
Up to 40 witnesses are expected to give evidence. The trial, before Justice
Gerald Nation, is expected to last two weeks.
