Lucasz Czapla appeared from custody at Edinburgh Sheriff Court on Monday where he faced a charge of assault and three road traffic offences
The 40-year-old has now reappeared on petition today where he faced a single charge of murder.
Czapla, from Edinburgh, made no plea during today’s private hearing and the case was continued for further examination.
He was remanded in custody and is expected to appear back in the dock within eight days.
On Monday, Czapla also made no plea to charges of assault and allegations of dangerous driving, driving while over the drink drive limit and failing to stop.
The court appearance follows the discovery of two-year-old Julius Czapla within a flat in Muirhouse Place West at around 9.30am on Saturday November 21.
The toddler was tragically pronounced dead at the scene a short time after the emergency services arrived at the scene.
Pictures of the Julius have been left along with floral tributes, candles, soft toys and cards near to his home by friends, loved ones and neighbours.
A Gofundme page has also been set up by a friend to help the family with funeral costs and living expenses.
The fundraising page says: “Thank you for visiting Support for Julius go fund me page.
“We tragically lost our beloved Julius, aged 2 years, on 21 November 2020.
“Friends and well wishers of Julius mum, Patrycja, have set this page to financially support her during this extremely unimaginable time.
“The contributions will go towards funeral expenses for Julius and what will be left will go towards Patrycja’s living expenses.”
A target of £3,000 has been set and so far the appeal has raised £1385 by generous well wishers.