Aleksander Vojneski, 31, is charged with killing Ms Conlon by stabbing her repeatedly in her Macgregor home in March 2012.

Ms Conlon was killed as a teenage boarder sat in the next room with headphones on playing League of Legends, an online computer game.

Vojneski and Ms Conlon had been in a rocky and allegedly violent relationship for six months, after meeting in Ward 2n, a psychiatric unit at Calvary Hospital in October.

Justice John Burns summed up the case to the jury on Monday, before they were eventually sent out to begin deliberations at 3pm.

The Crown's case against Vojneski, an ice user with mental health issues, is circumstantial.

They allege he became increasingly frustrated by failed attempts to get ice on credit while at Ms Conlon's home on the night of the murder.

Vojneski, the Crown says, had no money, while Ms Conlon was trying to wean him off drugs and had just spent the last of her own money on clothes from an online store.

Those clothes arrived on the morning of the murder, and a receipt for the purchase was found ripped up in the sink.

The timing of the murder is critical to the case, the court heard on Monday.

Crown prosecutor Shane Drumgold has argued the murder happened about 10.10pm, and that phone records put Vojneski at the house until at least 9.42pm.

Mr Drumgold said that time is supported by records of a particular game of League of Legends, played Ms Conlon's teenage boarder and his Sydney-based friend, in which both claim to have heard a scream.

The boarder has also given evidence that he was quite certain only he, Vojneski, and Ms Conlon were in the home, although he was wearing two sets of headphones in his room at the time.

Defence barrister Jack Pappas said the murder happened much later, at about 11.15pm, and highlights evidence of neighbours, who heard a scream, a car door shut, and the screech of a vehicle accelerating away.

Vojneski's fingerprint was found on a knife left in the kitchen, which the Crown allege was in the same knife block as the murder weapon, and his blood on the door handle and tiles outside Ms Conlon's room.

The Crown also allege he had violent tendencies, was quick to anger when he drank or used marijuana, and had a tendency to use and threaten people with knives.

The jury will continue deliberations on Tuesday.