A law professor says Lauren Dickason's defence team will be closely examining her five-week trial for any grounds to appeal against the verdicts.
In an 11-to-1 decision, the jury found Dickason, 42, was not insane and knew what she was doing when she attempted to strangle and then smothered her three children, in 2021.
She was found guilty of murdering two-year-old twins Karla and Maya and six-year-old Liane at their Timaru home in September 2021.
AUT law professor Kris Gledhill told Morning Report the fact the jury failed to reached a unanimous verdict would increase the likelihood of an appeal.
Gledhill said it was not unusual in New Zealand for a jury to be allowed to reach a majority verdict if a unanimous one could not be reached.
"Whenever juries can't agree, whenever 12 can't agree after a certain amount of time, judges allow them to come up with a majority verdict. It's a well-established part of New Zealand law, so it does happen on quite a few occasions.
"In this case, because she's potentially facing life imprisonment, her lawyers are going to be looking at the prospect of appeal in any event.
"... and obviously the fact that the Crown could not persuade all 12 jurors, that gives an extra ground for the defence lawyers to be looking around to see if there is a possible ground for appeal."
The judge has asked for a mental health assessment to determine the length and type of sentence.
Gledhill said the Sentencing Act stated that when someone was convicted of murder there was a presumption that the judge must impose life imprisonment unless it would be manifestly unjust to do so.
He said the judge would have to consider the medical evidence and decide: "Would it be manifestly unjust here to impose a sentence of life imprisonment?
"If he imposes life imprisonment, he's also got to set a minimum term for that life sentence - the minimum that would have to be served before any question of parole can arise.
"He's also got to decide whether to combine a sentence of imprisonment with an order that Ms Dickason be sent to a hospital in any event. So it's a fairly complex sentencing process as well."
"In this case, because she's potentially facing life imprisonment, her lawyers are going to be looking at the prospect of appeal in any event" - AUT law professor Kris Gledhill
Gledhill said an appeal could be made only after a sentence was handed down.
Dickason's lawyer, Kerryn Beaton KC, declined to comment.
Dickason, however, will not be extradited to her native South Africa - where her husband Graham Dickason is.
Deputy Prime Carmel Sepuloni told First Up because the crime was committed in New Zealand, Dickason would serve her sentence here.
The judge will decide at the sentencing hearing whether Dickason will go to jail, or be detained at Hillmorton Hospital's psychiatric unit.
Listen to the interview with Deputy Prime Carmel Sepuloni
Support for Timaru community
Timaru Hospital chaplain Reverend Alan said it would take the community years to heal from the Dickason family murders.
He had met Graham Dickason after the tragedy and organised a vigil of 300 people in the town days later.
Cummins told Morning Report the murders were a tragic loss, and there were no winners in the outcome of the trial.
He said there was a lot of sadness, prayers and goodwill in the community.
"People have had different reactions, different emotions. We'll just be keeping an eye out for ways in which we can offer support and friendship through the hospital community or through the wider community, through church networks."
"People have had different reactions, different emotions" - Reverend Alan Cummins