Police launched a homicide investigation after the remains were found at a property in Moncrieff Avenue in Clendon Park about 1.30pm on Thursday.
Detective Inspector Tofilau Faamanuia Vaaelua said the discovery was made after the residents “brought unowned property to their address”.
The residents were not thought to be involved, police said.
It is understood the residents went to the storage unit and picked up a trailer-load of goods, taking it home without realising its grim nature.
A trailer could be seen on the front driveway of the property while police investigated on Friday.
The storage company involved has been approached for comment.
On Monday morning, a family member at the property said they had been told to not talk to media by police but confirmed they had been offered victim support.
Neighbours of the property commented on the “wicked smell” coming from the home before police arrived.
One neighbour said her son had spotted a suitcase being removed from a trailer at the property by the house’s occupants.
She said the bags loaded off the trailer were put in a forensic tent. Detectives and forensic teams had been seen standing back in shock, she said.
A second neighbour said there had been a “wicked smell” in the area just after midday Thursday. As a former worker at Manukau crematorium, he recognised the smell as that of a body.
“I knew straight away and I thought where is that coming from,” he said, referring to the property.
Police arrived soon after and a hearse had been at the property, he said.