Danny Klobucar, 27, did not react as a jury handed down its verdict on Thursday afternoon, following a month-long trial in the ACT Supreme Court.

The jury's verdict means members found Klobucar to be the person who brutally fatally bashed Miodrag Gajic, 71, in the victim's Phillip unit on January 1, 2014.

But the jury has also agreed with overwhelming psychiatric evidence suggesting Klobucar was suffering a mental illness, namely paranoid schizophrenia, and was not able to properly understand that his actions were wrong.

That means Klobucar will be kept in a secure facility for a length of time yet to be decided by the ACT Civil and Administrative Tribunal.

Klobucar first met the victim two days before the murder, when he went with his uncle to buy cannabis from Mr Gajic.

He was obsessed with paedophiles and suffered delusions that he was working as a police agent to bust underground child molester networks.

He often became violent toward those he thought to be paedophiles, usually suspecting older men he came into contact with.

While outside Mr Gajic's unit, Klobucar noticed a blue Nissan Micra, asking his uncle whether it was the victim's.

He then said it looked like a gay car, that Mr Gajic was likely a paedophile, and that he probably had DVDs of him from his childhood.

Klobucar's mental health had deteriorated significantly in the lead-up to the killing. His mother told the court she had called police begging for them to help him.

A day after meeting Mr Gajic, Klobucar pestered his uncle for the address. His uncle, concerned by his nephew's behaviour, refused to give it to him.

But on New Year's Day, sometime between 10.40am and 11.10am, Klobucar returned to the unit.

He beat Mr Gajic to death, likely using a weapon, and delivering between eight to 10 blows to the head.

The Crown, represented by Mark Fernandez, had argued a strong circumstantial case proved that Klobucar was the killer.

Bloody footprints matching a set of Puma shoes he owned were found at the scene, while Mr Gajic's DNA was found on blood on the left shoe of that pair, which was seized from Klobucar's ute later that night.

The Crown argued that a witness had seen a man similar to Klobucar's appearance at the unit complex, driving a similar type of car, just before Mr Gajic's death.

It also put together a timeline, from CCTV cameras, a bus camera, and traced mobile phones, that it alleged put Klobucar at the scene at the time of the killing.

Klobucar's defence, represented by John Purnell, SC, and Ray Livingston, put forth two arguments. It said that Klobucar wasn't the killer, and that the prosecution hadn't proved he was beyond reasonable doubt.

But they also argued that there was a "mountain" of psychiatric evidence finding Klobucar was mentally impaired at the time of the killing.

Three psychiatrists, including one called by the Crown, made such a finding, and said he could not have properly understood that his conduct was wrong.

Mr Purnell used his closing address to tell the jury they would be acting "capriciously" if they were to go against the experts.

"It's all one way. It's overwhelming," he said on Tuesday.

"This young man was mentally impaired before the 1st of January, on the 1st of January, and after the 1st of January."

"He was suffering from paranoid schizophrenia."

Justice Hilary Penfold, who presided over the case, will now give an estimate of the prison sentence she would have imposed to the ACAT, who will use it to help decide how long Klobucar should be kept in a secure facility for.

She is expected to do that on Wednesday. Klobucar's case has been sent for urgent review by the ACAT.