Simeon of Durham names "Dolfin, Walther and Cospatric" as the sons of Gospatrick. He is named third of the three sons of Gospatrick by Roger of Hoveden. A memorandum dated to  records that "Earl Cospatryk formerly earl of Dunbar in Scotland had a brother Dolfin earl of Northumbarland…both…bastards", that they had "a legitimate brother Waldeve and a legitimate sister Etheldreda…of one father and one mother". It seems more likely that Gospatrick was his father’s oldest legitimate son as his father’s title was transmitted to his descendants.
Domesday Book records “Gospatric” holding numerous properties in Yorkshire. "Alexander nepos regis Alexandri, Beth comes, Gospatricius Dolfini, Mallus comes, Madach comes, Rothri comes, Gartnach comes, Dufagan comes, Willelmus frater regine, Edwardus constabularius, Gospatricius filius Walthef, Ufieth Alfricus pincerna" witnessed the charter dated to [1114/15] under which "Alexander…rex Scottorum filius regis Malcolmi et regine Margerete et…Sibilla regina Scottorum filia Henrici regis Anglie" reformed Scone Abbey. He appears to have held the position of an earl but is not referred to as such in any known document in his lifetime. Henry I King of England gave him the serjeanty of Beanley, Northumberland. "…Cospatrico fratre Dalfini…" witnessed the charter dated to  under which "David comes filius Malcolmi Regis Scottorum" founded the abbey of Selkirk. "…Gospatricius [frater] Dolfini…" subscribed the possibly spurious charter dated to  of "Alexander…Rex Scottorum…Sibilla regina Scottorum…". "…Cospatric frater Dalfin…" witnessed inquisitions by "David…Cumbrensis regionis princeps", dated 1124, concerning land owned by the church of Glasgow. "Cospatricu comite" donated "ecclesie sci Nicholai de Houm et…dimidium Gordune" to Kelso monastery by charter dated 22 Mar (no year) signed by "Cospatricius, Edwardus et Edgarus filios comitis et sponsa illud".
As "leader of the men of Lothian", he was killed in the battle of the Standard fighting the English. King Stephen confirmed the donation by "Gospatricio fr[atr]I Dolfini" of "terram Edmundi avunculi sui" and "terram Liolfi filii Uctredi" by charter dated Feb 1136. "David Rex Scotie" confirmed the grant of Coldingham by "Gospatricus comes frater Dolfini" to St Cuthbert by charter dated 1139.
The name of Gospatrick’s wife is not known. 1