The bodies of nine year old Conor, seven year old Darragh and three year old Carla McGinley were discovered in the Parson's Court, Newcastle house last Friday at approximately 7.45pm.
A woman has appeared in a Dublin court charged with the murder of her three children.
Earlier on Tuesday the father of the children said they all had "beautiful, bright futures" ahead of them and urged parents to "cuddle your children whenever you get a chance".
The woman was detained at Clondalkin Garda Station under section four of the Criminal Justice Act and could be questioned for up to 24 hours.
A woman in her forties was found by the gardaí near the scene, and has since received medical treatment at the Tallaght University Hospital.
In a brief statement released through An Garda Síochána, Ireland's police service, McGinley said: "There are no words".
Rocked by the tragic killings of the three children, the local Newcastle community have now come together to show their support for Andrew and the extended McGinley family. Every breath is a struggle. We are in touch with the family and they are aware and very thankful for this campaign.
He said Conor, Darragh and Carla had lovely, bright futures ahead of them. She was remanded to appear before the court this day next week.