The new details of family violence were heard as Ricardo Barbaro faced the Victorian Supreme Court for a pre-sentence hearing on Thursday.
The 37-year-old was last year found guilty of murdering his partner Ellie Price at her South Melbourne home in the early hours of April 29, 2020.
Police found her body five days later with stab wounds and a cut to her neck.
Prosecutor Damien Hannan said two months earlier, in February 2020, Barbaro and Ms Price had an altercation in a car at North Melbourne after spending the day drinking.
She "escaped" from the vehicle and Barbaro drove at her and group of other people who came to her aid, Mr Hannan said.
Barbaro pleaded guilty over the incident and was jailed for one month, the prosecutor told the court.
But Barbaro's barrister Rishi Nathwani said his client had pleaded guilty to the charge on the basis he did not assault Ms Price.
The barrister conceded there was an incident in November 2019 in which Barbaro damaged a car while Ms Price was inside because he was angry about not having contact with his children.
Mr Nathwani accepted that was a form of family violence, even if Ms Price was not directly hit.
The defence have also conceded family violence was an aggravating feature of the murder, as was the use of a knife and the stabbing happening in Ms Price's own home where she was entitled to feel safe.
He also noted Barbaro's conduct after the killing, where he left the scene in Ms Price's Mercedes Benz before dumping the vehicle at a Diggers Rest property, northwest of Melbourne.
Barbaro fled to NSW in a van after media reported that Ms Price's body had been found.
Justice Stephen Kaye said it was clear Barbaro's behaviour after the murder showed a "patent lack of remorse".
"It doesn't go to his credit at all," the justice said.
The pre-sentence hearing was adjourned for an assessment report from a neuropsychologist.
Barbaro was remanded in custody to his next court date in September.
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