Family spared
Miss Aim's parents and her brother arrived in New Zealand on Friday for the trial.
Her father Brian Aim said he, his wife Peggy and son Alan, had been spared having to sit through an expected four-five week trial.
Mr Aim praised the work of detectives involved in the investigation of his daughter's death, saying he believed the guilty plea was unusual.
"The outcome today would surely be thanks to the good police work within the New Zealand force," he told reporters outside the court.
Mr Aim last week told the Herald he wanted to find out how his daughter had died.
"The main question for me is how was Karen killed?" he said.
"Was she chased and terrorised, or was she clubbed from behind and never knew it had happened? I hope that question will be answered through the trial. It may not be but I am quite determined to hear as much as I can of the trial. I might not be able to face it."
Today he said the family intended on staying for Broughton's sentencing.
Mr Aim said his daughter's death had not destroyed his faith in New Zealand, saying he loved the country and he and his family had received many messages of support from people they didn't know.
A police officer found Miss Aim only 100m from her home bloodied and barely alive with her underwear torn, and immediately called an ambulance.
She was unresponsive and died shortly afterwards in Taupo Hospital.
At a depositions hearing, the officer who found Miss Aim told the Taupo Youth Court that he spoke to a detective about Broughton on the day she died.
Constable Matthew Barton said he gave the detective the address Broughton lived at - then 14 - within an hour of finding Miss Aim critically injured at 2.30am.
Mr Barton had been searching streets around the school for a vandal who had smashed windows on several classroom blocks when he saw "a female lying in a pool of blood".
Case shocked community
Broughton was taken in for questioning six days after Ms Aim was killed.
A search warrant executed at his home turned up a camera similar to Miss Aim's, along with a black handbag in an incinerator and a baseball bat with blood and glass embedded in it under the house.
Broughton had told police he spent the night of January 16 at home with his grandparents and later blamed the killing on a Mongrel Mob prospect from Rotorua.
He was arrested for her murder two months to the day after her death.
The murder rocked the Taupo community, and there was added shock when the age of the accused was made public.
After Miss Aim's death it soon emerged she was a popular and loved friend and family member.
She "loved New Zealand, she loved Taupo, she loved her job and she loved all her new friends", said her aunt Violet Perfect, who lives in Palmerston North.
Miss Aim's body was flown back to her home on Orkney, 19,000km away, soon after the murder and she was farewelled at a funeral service there attended by hundreds of mourners.
- NZHERALD STAFF and NZPA