Gabor Leslie Aranyi, 34, suffered severe mental health problems for over a decade, and was almost totally dependent on his carer and mother, Hungarian-born Ottilia Aranyi, 75.

The pair lived together in relative isolation at their Yarralumla home, and the mother helped him seek medication and support for his illness.

But, in what has been described as a moment of madness, Aranyi strangled his mother to death after she pestered him to go to an appointment with a mental health service on April 2, 2012.

He left her body lying on the kitchen floor and went to have a shower.

He returned to place a pillow under her head, but did not call an ambulance for almost seven hours.

Aranyi was found not guilty because of mental impairment earlier this month, with a number of reports showing he suffered delusions of grandeur and persecution, hallucinations and serious disturbances of thought, all consistent with paranoid schizophrenia.

But, despite the not guilty verdict, the ACT Supreme Court is required to indicate what sentence would have been imposed if Aranyi had been found guilty of murder.

Acting Justice John Nield began that process on Wednesday.

He remarked the "real tragedy of this case" was that the mother had gone to a mental health service the day before she was killed, seeking help for her son.

"What a tragedy it didn't happen that day," Acting Justice Nield said.

"It's quite obvious that she had been his real carer for many years, looking after his physical and mental health," he said.

"Then, in a moment of madness, he killed her."

Aranyi had believed he was a messenger of God, and that his mother was the devil.

His delusions were fuelled by cues such as the colour of his mother's car, seeing the 666 ABC Canberra frequency displayed on the radio, the shapes of the clouds and the belief he could influence events, both human and natural.

Aranyi's fate now rests with the ACT Civil and Administrative Tribunal, who will make orders about where he is to reside.

The Tribunal was due to meet later this afternoon, but must wait for Acting Justice Nield to indicate what sentence Aranyi would have faced if he had been found guilty of murder.

But the court has reserved handing down the sentence until Friday morning.