Police in Britain earlier confirmed that the woman's family had been informed of her death, the BBC reported. Ms Aim, 26, was as about far from home as it was possible for her be when she was murdered.
Her parents Brian and Peggy Aim live on the main island of the isolated group in the town of Holm, population 450.
News of their daughter's violent death had shocked the community.
Mr Aim, a builder, told NZPA he had been to New Zealand and thought it was a beautiful place.
"I loved the place, and so did Karen," he said.
Ms Aim was the "sweetest person" a friend said yesterday.
She was brutally attacked near Taupo's Nui-a-Tia College as she walked home from a night out in town.
She fell in love with Taupo on a visit in 2006, returning last October on a working visa.
Miss Aim was found in the early hours of Thursday with serious head injuries and died in hospital.
She was brutally attacked as she walked home from a night out in Taupo.
A friend of the woman told the Herald she was "the sweetest person I ever met".
The friend, who asked not to be identified, said the woman was on a working holiday from Scotland.
She had previously been in Taupo for a holiday, and had fallen in love with the place.
"She had come back to stay. But she had only been here six weeks or two months. She did not deserve this."
Police were last night making door-to-door inquiries and a large area, including one of the town's high schools, remained cordoned off.
They are also poring through CCTV footage from the town centre for clues.
Police have drafted in additional staff from the Waikato, Rotorua, Tauranga and Eastern Police District to bolster the Operation Waikato staff numbers.
In addition a Specialist Search Team arrived from Auckland today.
Inquiry head, Detective Senior Sergeant Greg Turner spoke to family of the dead woman overnight and Police are also speaking to relatives in the Manawatu.
"They were devastated by the news," he said.
Police have also interviewed the woman's flatmates as part of their homicide enquiry.
The area where Ms Aim was found murdered remains cordoned off. It is an area of five streets, a school and playing field.
Police say there have been increasing call outs in recent months for vandalism, violence and a robbery.
The woman was found about 2.30am yesterday by a police officer called to check a report of vandalism at the school.
Officers at the scene described it as a ghastly attack. The woman had extensive injuries, and it is understood she was bleeding heavily.
It is the first murder in Taupo in more than a year and happened on the eve of the A1Grand Prix motor racing event, which is expected to attract 40,000 visitors and will be broadcast to more than 150 countries.
Police called in from neighbouring districts to help with the motor racing were last night being reassigned to the homicide investigation.
The investigation is focusing on possible links between the school's smashed windows and the attack.
One neighbour near the school said he heard three male voices and a woman screaming in the early hours.
Detective Senior Sergeant Greg Turner urged those responsible for the vandalism to come forward.
"The longer they remain at large the more suspicion falls on them," he said. "It's a major whodunnit."
Police were unable to say last night whether she was sexually assaulted.
Ms Aim came to New Zealand in October 2006 and stayed for three months. She returned last October on a working holiday visa and had been working at Wairakei.
In the hours before her death, she was socialising in the town's bars. She was last seen about midnight in Mulligan's Irish bar.
She was found at the corner of Waikato and Motutahae Streets, near Taupo-Nui-A-Tia College, on the route between the town centre and the flat she shared with friends.
She was taken to Taupo Hospital, and died a short time later.
"We are trying to establish if she left the bar alone or not," said Mr Turner.
Police were trying to obtain security camera film from central Taupo "and further afield".
The inquiry could be complicated by the large number of visitors enjoying the summer heatwave.
Mr Turner said potential witnesses could have left on tourist buses yesterday morning.
It was also "entirely feasible" that someone involved could have left town, he said.
The murder came hours after Taupo mayor Rick Cooper announced a council plan to improve security in the town.
- with NZPA, NZ HERALD STAFF
