Post-mortem examinations have now been carried out on the bodies of all three men found dead near Kanturk in County Cork on Monday.
Tadhg (59) O'Sullivan and his sons Mark (26) and Diarmuid (23) were discovered with gunshot wounds on the family farm on Monday.
Gardaí are trying to piece together the sequence of what happened - and are investigating if the triple shooting was over of a dispute about land and inheritance.
Officers in Kanturk have said they are not looking for any other person in connection with the tragedy, but they are appealing for witnesses.
All three post-mortems have now been carried out; however, Gardai will not be disclosing any detail on what was found.
As part of their investigation, Gardaí are examining a note which was found near one of the bodies.
A file will now be prepared for the DPP and the Coroner.
On Newstalk Breakfast this morning, Ralph Riegel, Southern Correspondent with the Irish Independent, said the investigation was continuing.
"You had two post mortems conducted yesterday at Cork University Hospital on the bodies of Tadhg - the 59-year-old father of two - and Diarmuid - his youngest son who was 23-years-old.
"This third post mortem will take place at CUH today, and that'll be on the body of Mark O'Sullivan.
"Gardaí believe that this post mortem will be particularly significant because it's understood that the father and the youngest son died from single gunshot wounds.
"But they want to know whether there was possibly more than one gunshot received or suffered in respect of Mark.
"Mark's body was found in the bedroom of the farmhouse; the other two bodies were recovered about 600 metres away from that property.
"Beside the two bodies that were found were two rifles, and a total of three firearms are currently being examined by ballistic experts in Dublin: two rifles and a shotgun.
"Forensic experts also conducted an exhaustive examination of the two scenes yesterday, and Gardaí basically said that they're very happy with how the investigation is proceeding.
"They've already said they're not looking for anyone else in connection with this - but they're quite hopeful that the results of the forensic tests, ballistic tests and the post mortem examinations will help somehow explain to them the sequence of how this tragedy unfolded."
He also said documentation has been examined within the house "which does indicate there was a dispute over the inheritance of this 140/150 acre farm".
"That unfortunately seems to have been the spark that led to this appalling event".
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