Þorbjörn / Thorbjorn 'loki' Böðmóðarson

1. RAGNVALD "the Wise", son of EYSTEIN "Glumra/Clatterer" Jarl in Norway & his wife ---] (-[894]). Orkneyinga Saga names “Eystein the Clatterer, father of the wise counsellor Earl Rognwald the Powerful…”, adding that “Earl Rognwald campaigned with King Harald Fine-Hair who gave him charge of North More, South More and Romsdale”[784]. Snorre names "Ragnvald Earl of More, a son of Eystein "Glumra" when recording that he had become a supporter of King Harald who had invested him with the districts of North More and Raumsdal[785]. Snorre records that he was created Jarl of North and South Möre and of Raumsdal in Norway by Harald I "Hårfagre" King of Norway after his victory at Solskiel [869] against Hunthiof King of Möre and Nokve King of Raumsdal[786]. Orkneyinga Saga and Snorre both record that King Harald granted Shetland and Orkney to Ragnvald in compensation for the death of his son Ivar[787]. The Historia Norwegie records that "principi Rogwaldi" crossed the Solund Sea, destroyed the peoples of the Orkney islands, in the days of "Haraldi Comati regis…Norwegie"[788]. Snorre records that Ragnvald was ambushed in his hall and burned alive by Halfdan Haaleg and Gudred Liomi, two of King Harald's sons[789]. (Cawley's Medlands)

a) for other children: see Cawley’s NORWEGIAN NOBILITY.
b) HALLAD . Orkneyinga Saga names “Hallad, Hrollaug and the youngest Einar” as “natural sons” of “Earl Rognwald”[790]. Snorre names "Hallad, the second Einar, the third Hrollaug" as the three sons of "Earl Ragnvald" by concubines, adding that they were all "grown men" when their legitimate brothers were still children[791]. Jarl [of Orkney]. Orkneyinga Saga records that Ragnvald sent “his son Hallad west to the islands” after hearing of the death of his brother and nephew, and that Harald I "Hårfagre" King of Norway gave “the title of earl” to Hallad who “came to Orkney and took up residence on Mainland”[792]. Snorre records that Earl Ragnvald installed his son Hallad as Jarl of Orkney after the death of his brother Sigurd, but that he resigned the earldom and returned to Norway[793]. Orkneyinga Saga records that, following complaints by farmers about Viking raids, Hallad “tiring of his rule, gave up the earldom and went back to Norway as a common landholder” which “made him a laughing stock”[794].
m ---. The name of Hallad´s wife is not known. (Cawley's Medlands)
Hallad & his wife had one child:

i) THORE. Are´s Landnama-book records that "Thor-rid the daughter of Thore, the son of Earl Hallad, the son of Rogn-wald Earl of More" married "Thor-gils…"[795]. (Cawley's Medlands)

(a) THOR-RID . Are´s Landnama-book records that "Thor-rid the daughter of Thore, the son of Earl Hallad, the son of Rogn-wald Earl of More" married "Thor-gils of Thor-gils-stead in Deep-frith, the father of Coll", son of "Thor-beorn Loke…the son of Bead-mod of Scut [who] went to Iceland and took in settlement Deep-frith and Gruoch-ness, up to Gowe-frith", and names their descendants[796].
m THORGILS, son of THORBEORN Loke & his wife ---. (Cawley's Medlands)