Opening the Supreme Court appeal, Mr John Gordon SC, for The Irish Times Ltd, said the appellants would say that, while the trial of the accused was now over, the order made by Judge Murphy set an extraordinary precedent.
Counsel said the judge had made the order of his own volition and had not sought the views of the parties in the trial.
There were other means of dealing with the situation other than imposing a blanket ban.
He contended that the trial judge could never pre-empt media coverage or make a pre-emptive order of the type made, and that Mr Justice Morris had inaccurately concluded that he was not entitled to interfere with that order.
Mr Gordon submitted that fair and accurate reporting could not prejudice a fair trial.
He said Judge Murphy had no jurisdiction to do what he did, and if there was ever to be any jurisdiction to interfere with the rights of the media to report contemporaneously on a trial, it must occur only in the most rare of circumstances.
Mr Frank Clarke SC, for Independent Newspapers, said Article 34.1 of the Constitution precluded jurisdiction of the type exercised by Judge Murphy.
He said Article 34.1 stated: "Justice shall be administered in courts established by law by judges appointed in the manner provided by this Constitution and, save in such special and limited cases as may be prescribed by law, shall be administered in public."
This made clear that the right to have justice administered in public could only be interfered with in "special and limited" cases.
Mr Clarke said the effect of this was that, in the absence of a statute, a case must be conducted in public. He asked whether a case could be properly said to be conducted in public where the public, as a matter of practicality, could not get to know what happened.
He said Judge Murphy was incorrect in taking the view that the court has a residual discretion in cases where a conflict of constitutional rights might exist.
Mr Paul O'Higgins SC, for RTE, said if the court found that Judge Murphy had jurisdiction to make the order banning or postponing contemporaneous reporting, that jurisdiction must exist only in the most limited circumstances. Where the court was dealing with two competing constitutional rights, it must do so in such a way as to preserve the best part of both.
Mr O'Higgins submitted Judge Murphy's action was "wholly over-protective" if for "the very best of reasons" - to protect the rights of those accused.
Mr Denis McCullough SC, for Examiner Publications, submitted that for a case to be heard in public means the press should be entitled to be present and to report it contemporaneously and fairly and accurately. His clients were entitled to the presumption that no members of the press would report it unfairly and inaccurately.
Ms Mary Finlay SC, for Judge Murphy and the Attorney General, submitted that the judge had jurisdiction to make the order made.
She submitted that Mr Justice Morris was wrong to conclude that, because of the order made, the trial was not being held in public.
She said it was "not appropriate" for the Attorney General to make any observations on the correctness or otherwise of the actual order. Judge Muprhy had formed the view that, in his judgment, it was necessary to make the order to avoid the possibility of a trial being aborted as a result of media coverage.
Counsel said the appellants were wrong in contending this was not a trial in public and that the right of the media to contemporaneously report every piece of evidence was an essential part of holding a trial in public.
Mr Aindrias O Caoimh, for the DPP, said he was supporting Ms Finlay's submissions on behalf of the Attorney General.
The hearing resumes today.