"Are you appearing in this court or are you running your case in the media?" former NSW District Court chief judge Reginald Blanch QC asked Jeremy Morris SC, who is representing Kathleen Megan Folbigg, on Monday.

Mr Blanch said the situation was appalling and noted "in the ordinary course of events" it would be considered contempt of court.

A published ABC article includes material that was not tendered at any preliminary hearings and will be not be admitted into evidence at the inquiry into Folbigg's convictions.

"Your Honour, I will make some inquiries," Mr Morris said at the Lidcombe coronial complex.

Folbigg was jailed for at least 25 years in 2003 after she was found guilty of killing her four babies - Caleb, Patrick, Sarah and Laura - in the decade from 1989.

Her children all died at home aged between 19 days and 19 months.

The NSW government agreed to a judicial review of her case in August 2018 and hearings began on Monday.

The 51-year-old has confirmed in writing she will testify on April 17 and 18. She didn't take the stand at her trial.

"Ms Folbigg is allowed to give evidence ... about the diary entries, possession of the diaries and her disposal of the diaries," counsel assisting, Gail Furness SC, said in her opening address.

She cited various entries by Folbigg which were presented to the jury as circumstantial evidence.

These included comments about baby Sarah who "left, with a bit of help" and Laura being "a fairly good-natured baby" which "saved her from the fate of her siblings".

"I think she was warned," Folbigg wrote in December 1997.

Laura died in March 1999.

The inquiry is focused on medical advances and new research - including multiple infant deaths in the one family attributed to unidentified natural causes.

The crown prosecutor in 2003 submitted "it has never been recorded that the same person has been hit by lightning four times" and "I can't disprove that one day some piglets might be born with wings and that they might fly. Is that reasonable doubt?".

The judge directed the jury that sudden infant death syndrome deaths were rare and while there was no authenticated record of three or more such deaths in one family that didn't mean it was impossible.

Professor Rosemary Horne on Monday testified SIDS itself was rare but "the general consensus seems to be that more than one SIDS in a family is very rare".

"I have asked my colleagues ... in the UK and USA and none of them could recall having three or more deaths in a family," the Monash University paediatric researcher said.

Both she and Professor Dawn Elder, who heads paediatrics at New Zealand's University of Otago, gave evidence that all four of Folbigg's children had a low risk of SIDS.

Mr Blanch will prepare a report on the inquiry's results for the NSW governor.

If the judicial officer feels there's reasonable doubt over Folbigg's guilt he can refer the matter to the Court of Criminal Appeal.

Folbigg will, at present, be eligible for parole in April 2028. The inquiry continues.

Australian Associated Press