A portion of the original kingdom was made part of County Kildare.
With the death of Somairle, Gofraid returned from exile to reclaim Mann, and outer-island portion of the kingdom.
So I will give you land in Caithness - a portion of the kingdom granted me by Malcolm, King of the Scots.
For example, during the 11th century reign of Godred Crovan, his son Lögmaðr appears to have governed the northern portion of the kingdom.
Cylarabes regained the portion of the kingdom given to Bias upon the death of Cyanippus.
Even within the remaining portions of the kingdom, there were still powerful and violent rivalries.
The northernmost portions of the former kingdom, including the town of Osnabrück, had become part of the states of Hanover and Oldenburg.
There were times when there was no one supreme king of Airgíalla, two or more kings ruling portions of the kingdom.
He later returned to Deheubarth and ruled a portion of the kingdom, but was forced to flee to Ireland again in 1127.
Olaf returned to Norway in the spring of 1067, claiming his portion of the kingdom.