The Central Criminal Court has ordered Facebook and Twitter to remove any photographs or any other material identifying the two boys convicted yesterday of the murder of 14-year-old Ana Kriégel.
The court also allowed the Director of Public Prosecutions to serve notice on the two companies that she intends to seek orders for the attachment of the companies' assets and the committal to prison of those responsible for publishing the material for contempt of court.
That application will be back before the court tomorrow.
Mr Justice Michael White said the publication of anything identifying the two boys was a breach of the Children Act and of the court's orders.
He said no individual had the right to put anything on social media identifying or tending to identify the teenagers.
He said anyone who decided to try to identify the people convicted would be subject to a contempt of court application and the matter would be treated in the most serious fashion.
The matter was raised by prosecution lawyer Brendan Grehan, who said issues on social media had been drawn to the attention of the DPP's office by lawyers for Boy B.
He said those posting the material were capable of being identified, but the material had been shared and the DPP did not know to what extent.
Mr Grehan said the DPP was conscious of the concept of something going viral and took the view that the operators of Facebook and Twitter had a responsibility in the matter.
He said those posting material were engaged in a "fairly wilful disregard" of the provisions of the Children Act and the orders of Mr Justice Paul McDermott.
And he said he wanted the court to state loud and clear that it had unlimited powers to imprisonment, fine, attach and sequester the assets of anyone who defied the court's orders.
Mr Grehan said neither individuals nor corporate bodies could flout court orders.
Gardaí have also warned the public that publishing pictures or any other material identifying a child appearing before the criminal courts is a breach of the 2001 Children Act.
Anyone convicted of doing so can be jailed for up to a year and fined up to €1,500 if the matter is dealt with in the district court. If the matter goes to a higher court, a person can be jailed for up to three years and fined up to €10,000 for breaching this provision.
In a statement, a Facebook spokesperson said as soon as they became aware of content identifying Boy A and Boy B being shared on Facebook, they removed it immediately for violating their community standards and local law.
The spokesperson said it also applied photo matching technology to prevent the content from being reshared on Facebook, Instagram or Messenger. The spokesperson said it would continue to remove this content from its platforms.