The school where two of the McGinley children, who died on Friday, attended has described them as "wonderful boys".
In a statement, School Chrónain said "we are all deeply saddened by the sudden death of two of our pupils Conchúr and Darragh Mac Fhionnghaile and their sister Carla. It is a tragedy for our community."
It extended its sympathy to the families involved.
The bodies of Conor aged 9, Darragh aged 7 and Carla aged 3 were found in a house at Parson's Court in Newcastle village, northwest of Rathcoole on Friday.
The school said that Conor (Conchúr) was a pupil in Rang a Trí while his younger brother Darragh was in Rang a hAon.
"They were both wonderful boys and it was a pleasure to have them in our school. They will be greatly missed by all who knew them", the statement said.
The school has now implemented its Critical Incident Management Plan.
The school says psychologists from the National Educational Psychological Services have been liaising with them over the weekend and will continue to support and advise them in the coming days.
The school will remain open and has asked for privacy at this time.
Gardaí were called to a house at Parsons Court at about 7.45pm last Friday night and first found a woman on the street in a disorientated state.
The woman in her 40s, who is the children's mother, was admitted to Tallaght University Hospital, where she continues to receive medical treatment .
Gardaí entered the house and found the bodies of the three young children. A note was also found at the scene.
Gardaí said they were not looking for anyone else in relation to the incident.