Note: from Kevin Walters:

See bk&q chart 28, NB21, pp 398, 401-2, 426, 450, 495

p 450 Paul was the elder son of Thorfinn II and inherited the earldom with his brother Erlend II. It is possible that both were installed as earls of Caithness in 1057, prior to Thorfinn's death, suggesting that the earldom may have become regarded as a title for the heir(s) apparent. We do not know for certain when Paul was born, but it was probably about 1038. Already by that date Thorfinn was professing his Christian beliefs by naming his first-born Paul, unless he was not christened until Thorfinn's visit to the pope in 1048. When the brothers inherited the earldom they ruled it jointly and did not divide the lands or revenues between them. It seems they worked well together and generally agreed in all their actions. Soon after their father's death, Harald Hardraada, the king of Norway, arrived in the Orkneys prior to his invasion of England. He raised additional levies from amongst the earldom, which stretched as far as the Western Isles, and when he sailed for England in 1066, he was accompanied by both earls. Although Harald was defeated by Harold II of England at Stamford Bridge in September 1066, the two earls survived and returned to Orkney with Harald's son, Olaf, who remained with them during that winter before returning to establishing himself as king of Norway the following year. It is evident that they did not believe they had authority over all of the Western Isles, since they were not involved in the usurpation of Man by Godred Crovan in 1079. For most of their reign the two earls governed wisely and continued to develop and promote the bishopric of Orkney, but by the year 1090 or so a rift occurred between them over the amtitions of their respective sons, especially Paul's son Haakon. Haakon was eventually banished from Orkney in 1093, and he stayed in Norway and Sweden for the next few years. It was he who encouraged Magnus III of Norway to visit his estates in the western seas and this planted the idea of Magnus installing his son, Sugurd III, as king of the Orkneys, using the islands as an appanage for the heir to the throne. Magnus sailed to the Orkneys in the spring of 1098 and deposed the two earls, despite the care they had shown to his father Olaf. The earls were taken in captivity back to Norway where they both died within the year, Paul at Bergen and Erlend at Nidaros.