As with his predecessor Findláech mac Ruaidrí, sources call him "King of Scotland."
The Orkneyinga Saga for instance tells us that Thorfinn Sigurdsson, Earl of Orkney was the son of the daughter of Máel Coluim, king of Scotland.
His death date derives from the Annals of Tigernach, which notes s.a. 1029, "Mael Colaim mac Mael-Brighdi mac Ruaidrí, rí Alban mortuus est (="Máel Coluim, son of Máel Brigte, son of Ruadrí, King of Scotland, dies")."
As can be seen, if it were not for the mac Mael-Brighdi, we could easily assume we were being given an inaccurate date for the death of King Máel Coluim II.
Máel Coluim mac Máil Brigti seems to have been succeeded by his brother Gille Coemgáin.