His body was removed from the Housing New Zealand complex last night and will undergo a post-mortem examination today.
Neighbour Samantha Saia told the Herald that Mulholland, who she knew as "Mike", was a nice, friendly man.
"I just don't know who would do such a thing," she said.
"It's just so sad."
Saia said Mulholland lived alone, but had regular visitors.
There was never any trouble on the third floor and most of the residents in that block were older and knew each other.
"He was pretty quiet ... why did they kill him?" she said.
"He was a nice man, he was a nice person."
Yesterday a team of police combed the building and surrounds for clues about Mulholland's death.
They could be seen fingerprinting doorways, banisters, walls and placing evidence markers in the grassy area in front of Mulholland's block.
A 29-year-old man was last night helping police with their inquiries.
He had not been arrested but police had not ruled out the possibility of charges being laid.
Earlier in the day police released a photograph of the 29-year-old - captured on CCTV cameras in Mulholland's building - and appealed for information about his identity.
About three hours later two police officers driving on Karangahape Rd in central Auckland spotted the man, and took him to the station to be interviewed.
Detective Inspector Scott Beard said it was unclear how Mulholland suffered his fatal injuries, what the motivation for the attack was or if a weapon was used.
It was also unclear if the victim knew the man in the CCTV footage or whether anything in his apartment was missing or disturbed.
Beard said the investigation was in its early stages and a number of detectives were working to piece together what happened to Mulholland - and why.
"We want to assure our community that we undertaking a thorough investigation to establish what has happened," he said.
