A man who was left alone with his partner's toddler beat the boy to death and lied about how he received his injuries, prosecutors have told South Australia's Supreme Court.

Brock Michael Powell, 24, is standing trial charged with the murder of two-year-old B.J. Williams, who died in January 2012.

Powell has elected for his case to be heard by a judge without a jury.

Prosecutor Sandi McDonald said the toddler died from head trauma and also sustained bruising to his face, body and genitals.

Ms McDonald told the court Powell was alone with the toddler at a granny flat at Melrose Park in Adelaide's south where he lived with the boy's mother.

She said Powell was in a relationship with the toddler's mother and the pair had argued shortly before the boy was injured.

The court heard Powell was agitated and the toddler's mother left the granny flat to go into her own mother's house on the same property.

"At some stage after that she was awoken by the accused. He told her something was wrong and BJ wasn't breathing," Ms McDonald said.

The court heard the toddler's mother ran to the granny flat and saw Powell attempt to give the boy CPR.

An emergency call was made but the pair decided to take the boy to the nearby Flinders Medical Centre.

"Staff immediately observed bruising to his head and face," Ms McDonald said.

"They managed to stabilise his condition and he was transferred to the Women's and Children's Hospital intensive care unit, but nothing could be done and life support was turned off the following day."

Ms McDonald said Powell had told hospital staff, the toddler's family and police that the boy had suffered a fall in bed and had become wedged between the base of the bed and a wardrobe.

"It's the prosecution case that the accused did not and has not told the truth about what had happened to BJ," she said.

She said the nature and number of the toddler's injuries were inconsistent with Powell's story.

The court heard the toddler suffered blunt force trauma to his head and had extensive bruising on his scalp, eye socket, cheeks, ears and jaw.

His torso, elbow and genitals were also badly bruised.

"It's the prosecution case that these injuries didn't come about by a fall of about 30 centimetres onto a carpet floor. This child had taken a beating and it was the accused who did that," Ms McDonald said.

"It could not have happened the way the accused had described to so many people. The only other logical inference based on the evidence is that he beat this little boy to death."

The court heard the toddler's mother will be called as a prosecution witness and there will also be expert evidence about the child's injuries as observed by a paediatrician at the Women's and Children's Hospital and the forensic pathologist who conducted the autopsy.

A video of a police interview with Powell, conducted at the hospital, will also be played to the court.

The trial is being heard by Justice Timothy Anderson.