A man felt "overwhelmed at being a father" when he shook his toddler son, causing him fatal head injuries.
The man pleaded guilty to manslaughter at a court hearing today. He was granted interim name suppression, meaning the child cannot be named.
The toddler died in Starship Hospital from head injuries in 2015, after being transferred there from another hospital.
According to the summary of facts, made available to media at the hearing, the man felt "overwhelmed at being a father and having to care for [the boy] as often as he did".
It said he woke in the middle of the night and shook his son so violently he caused the boy to stop breathing.
"He picked [the boy] up and shook him with sufficient force to cause head injuries that ultimately led to his death."
An autopsy found the toddler died of head trauma, which disrupted the blood supply to his brain.
He had bilateral retinal haemorrhages, causing blindness in both eyes, the summary said.
Experts confirmed the injuries were consistent with the child being shaken, but it was difficult to quantify "the precise level of force" required to inflict the injuries the boy sustained.
The man will be sentenced in March.
The judge today gave the man a first strike warning under the "three strikes" legislation for violent offenders.