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Maqbool Hussain, 49, was found dead by relatives in a temporary squat in Balmoral after suffering what police describe as a violent death.
A homicide investigation, codenamed Operation Gridley, has been launched.
Mr Hussain was originally from Pakistan but had lived in New Zealand since 1992.
He had been living in a partially enclosed garage storage area of a former green grocery at 660 Dominion Rd for the better part of a year, and was known to frequent local businesses along the road, police said.
A scene examination at the site was completed early this afternoon.
Officer in charge of the homicide investigation, Detective Inspector Chris Cahill, said Mr Hussain had been fatally assaulted sometime between 6.30pm on Saturday, March 22 and midday on Monday, March 24.
"We have spoken to people who saw Mr Hussain alive in the early evening of Saturday the 22nd and we're obviously very interested in hearing from anyone who has information about who he might have had interactions with recently.
"Mr Hussain is survived by an estranged wife and daughter who live overseas but had regular contact with relatives and acquaintances in the Balmoral neighbourhood.
"While he had hit hard times and lived in what some would call rough circumstances, our inquiries to date lead us to believe his lifestyle was comparatively routine and his living area was organised and clean.
"Our focus right now is on the victim's family and trying to narrow down the time Mr Hussain was killed and, of course, identifying who killed him.''
Police were continuing inquiries along Halston St and Dominion Rd today, and urged anyone with information to contact them by calling (09) 820 5763, texting 021 191 2865 or emailing email@example.com
Information could also be provided anonymously through Crimestoppers on 0800 555 111.