A grandmother accused of smoking meth and then murdering an Auckland toddler because he was too hard to toilet train is now waiting as a jury decides her fate.

Kathleen Elizabeth Cooper, 65, is standing trial in the High Court accused of murder by throwing her grandson down the hallway of their Manurewa home after a toileting accident on December 13, 2015.

Suffering serious head injuries, two-year-old Jermain Mason Ngawhau was rushed to Starship Hospital for emergency surgery, but died five days later.

On Monday, the jury of seven women and five men retired to begin deliberating their verdict.

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Earlier, Justice Sarah Katz told them there was no dispute Cooper killed Jermain.
Prosecutors and Cooper's lawyers agreed she had thrown the toddler, causing the injuries that killed him, and so was guilty of manslaughter.

She said the key question for the jury to consider was whether Cooper had intended to kill Jermain and was consequently guilty or not of the more serious charge of murder.

The Crown had argued Cooper was guilty of murder because she knew better than anyone Jermain was a frail toddler who could not yet walk and yet she threw him in a way she knew could kill him, she said.

Prosecutor Aaron Perkins QC said Cooper had become increasingly angry and overwhelmed by the challenge of caring for her troubled daughter's four children, all aged under five.

He said she took to regularly hitting them, with Jermain - whose delayed development made him slow to learn to use the toilet - found to be covered in numerous old and fresh bruises, Justice Katz said.

To make matters worse, Cooper was a meth user prosecutors, according to prosecutors, she said.

However, Cooper's lawyer Paul Dacre QC argued she did not intend to kill Jermain. He said while Cooper's parenting methods and foul language were questionable, she kept her grandkids well fed and clothed.

She had originally agreed to care for them when she was a 62-year-old woman well into retirement, and Mr Dacre questioned how this could turn into murderous hatred just 18 months later.

He also contested the evidence that Cooper had smoked meth in the week leading up to Jermain's death, saying the Crown had not proven this.

- NZN