He had been in a long-term relationship with Ms Elder-Holmes, the adopted daughter of broadcaster Sir Paul Holmes who died from cancer last year.
Information gathered since early this morning is that a group of people Mr Morris was associated with were walking to a service station to purchase refreshments, police said in a statement tonight.
"They have walked past a party and an altercation has then taken place and a fight has broken out."
Police believed around 25 to 30 people were involved in the altercation.
"There is currently nothing to suggest that the fight was the result of any gang tensions and police can confirm that it did not occur at a gang address.
"At this early stage of the investigation police believe this was a random incident, and the victim was not specifically targeted."
Two people were arrested at the scene for disorder-related offences however no charges have been laid.
Other people were injured in the altercation, Detective Inspector Greg Cramer said. "There were a number of minor injuries consistent with a fight."
Specialist Police searchers working near to the scene of a incident on Don Buck Road, Massey. Photo / New Zealand Herald / Sarah Ivey
A large team of police are working on the case and officers remain at the scene of the incident this evening. A forensic examination has been underway since the early hours of the morning.
A post mortem examination has concluded that Mr Morris sustained a head injury, police said.
"A weapon is believed to be involved but exactly what type of weapon is yet to be determined."
One of the key elements of the investigation was to determine exactly who and how many people were involved, police said.
"When police arrived at last night's scene there were around 15 people on the road, and it is believed that up to another 15 people were at a nearby address.
"Mr Morris's family are understandably traumatised and police and Victim Support are continuing to offer assistance in this regard."
Police were called to the scene around midnight following reports that a group of people were fighting.
Emergency services arrived soon after and found Mr Morris was seriously injured. He was treated by paramedics in the ambulance, but died on the way to hospital.
Mr Cramer said police were speaking with a large number of people who were in the area at the time.
"Anyone who may have information that can help us is asked to call the Henderson police.
"If you wish to be anonymous you can call Crimestoppers on 0800 555 111."
Mr Morris and Ms Elder-Holmes, who celebrated their sixth anniversary together in June, have spoken previously of their long battle against drug-addiction and troubles with the law, and their love for each other pulling them through that dark period.
Mr Morris and Ms Elder-Holmes' friends and family took to social media this morning.
Police are guarding the scene of a incident in Don Buck Road, Massey. Photo / New Zealand Herald / Sarah Ivey
His brother, Calen Morris, vented on Facebook: "my big hearted little brother was murdered last night. from hoodlums with f**ken knifes and s*** lives ... rot in hell".
"im sorry but people need to ... teach your f***en kids right from wrong! i love my family and im sorry i wasnt there c.morris."
"be strong morris crew and ill see you all soon. only the good die young! im keeping my cool right now ... "
Rikki Hewitt tweeted: "Omg really feeling for Millie Holmes right now :( RIP Conner."
The owner of a shop near the house where Mr Morris died said there hadn't been trouble there before.
People passing the scene said they were shocked by the incident.
"Is that the fifth [homicide] out here? Too many, too many," one man said.
In 2012, Ms Elder-Holmes told Metro she would not have been able to fight her P addiction and turn around her life around without Mr Morris. They eventually became clean without professional help by living a hermit-like existence -- eating, sleeping and watching TV -- in their west Auckland flat.
"Connor is my biggest fan. He gets so excited and proud of me for my (Facebook Clean Eatz NZ) page," Ms Elder-Holmes said in March this year.
They had recently been on their first overseas trip together -- Asia, Dubai, Italy, Paris, Amsterdam and Greece.