Thorfinn was the youngest son of
Torf-Einarr, himself the son of
Rognvald Eysteinsson, the first Earl of Orkney. Torf-Einarr had two other sons, Arnkel and Erlend who "fell in a war expedition" at an unspecified location in England along with
Erik Bloodaxe, who was Torf-Einarr's kinsman through his sister Álöf who was married to Torf-Einarr's brother Thorir. Erik's widow,
Gunnhildr then fled north to Orkney with her sons who used the islands as a base for summer raiding expeditions. each of whom had a son called Einar - Einar
kliningr ("Buttered-bread") and Einar
harðkjotr ("Hard-mouth"). Gunnhildr and her family later set out for Norway, but before they left they "gave" their daughter
Ragnhild Eriksdotter to Arnfinn Thorfinnsson in marriage. In the later days of Thorfinn's rule, the sons of
Eric Bloodaxe fled Norway and returned to Orkney where they "committed great excesses". ==Death and legacy==