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Expatriate New Zealander Robert Wilkinson, 64, known as Murray, was stabbed outside a caravan parked in the driveway of a Waihi Beach home early on January 1.
He died in the intensive care unit of Waikato Hospital yesterday.
His son, wife and daughter fronted media at a press conference in Hamilton today.
Dan Wilkinson said the family were "desperate to understand" what had happened to his father.
"Somebody has the answer to my dad's death," he said.
"If you know anything - anything at all, please let the police know."
He said the family had been robbed of Mr Wilkinson's love and while they appreciated the public focus in finding the killer and helping police, they wanted to grieve privately.
Mr Wilkinson's daughter Cory Rance and widow Luise were at the press conference but were too distraught to speak publicly.
Detective Inspector Chris Page said police were still seeking the weapon used to kill Mr Wilkinson, who lived in Queensland, and had widened the area they were searching. It is unclear what kind of weapon was used, he said.
A post-mortem examination of Mr Wilkinson's body was to be completed in Auckland today.
Thirty police staff are working on the homicide investigation as they hunt for the attacker, who fled the scene when neighbours heard a disturbance.
Checkpoints were set up at Waihi exit-points on Wednesday for police to talk to holidaymakers as they left the area and they have also asked New Year's Eve partygoers to supply their festive photographs in the hope the pictures identify the attacker.
Waihi Beach's normal population is about 3000 but swelled to 16,000 over the festive period.
When the attack occurred, officers were moving on large numbers of mostly young people from the area around the surf club, the motor camp, Beach Rd and Ocean View Rd.
Information for the Operation Brad investigation Can be left with police on 07 858 6200 or anonymously with Crimestoppers on 0800 555 111.
- By Anna Leask of the New Zealand Herald