News organisations, including the owners of the Irish Independent, have appealed the decision of a High Court judge to ban the media from naming a mother who smothered her three-year-old daughter with a pillow.
The judge had ordered that the deceased child should not be identified and, as a consequence, the woman cannot be named as to do so would identify the dead child.
The woman was last year found not guilty by reason of insanity of murdering the toddler at her family home.
At the outset of her trial in October, prosecuting counsel Paul Murray SC applied for an order preventing publication of anything that might identify the deceased child.
He said that, under Section 252 of the Children Act 2001, it was an offence to publish anything that could identify a child who is an alleged victim of an offence.
Mr Justice Michael White agreed to make the order but the following day a lawyer representing several media outlets applied to trial judge Ms Justice Carmel Stewart to set it aside.
On hearing arguments from both sides, Ms Justice Stewart said that the wording of Section 252 of the Act was clear, and that it was appropriate to continue with the reporting restrictions.
The media organisations, namely Independent News & Media, RTÉ, News Group Newspapers Ltd and 'The Irish Times', yesterday appealed that decision to the Court of Appeal.
Their barrister, Luán Ó Braonáin SC, told the court the deceased was no longer a child at the time of the proceedings.
Counsel said that while it had already been published that the accused had killed her child, the media were then unable to publish the fact that the deceased did not die as a result of an offence carried out by her mother.
He said that the purpose of Section 252 appeared to be to mitigate the harm and secondary victimisation of children in court proceedings, and so that they would be able to progress with their lives.
"Those are interests that do not arise in relation to the deceased," he said. "A distinction therefore falls to be made."
Diarmaid McGuinness SC, for the woman and the DPP, said the deceased had continued to be a child after death.
"In my submission, the Oireachtas intended to protect children who were murdered from the type of publicity that arises," he said.
The three-judge Court of Appeal reserved judgment in the case.