Asgall (Askulf; Hasculf) (d. 1171), son of Ragnall and ruler of Dublin, belonged to the Hiberno-Scandinavian line of Torcall (Thorkell), which had emerged to rule Dublin in the person of Thorkell, grandfather of Asgall, following the failure of Conchobar Ua Conchobair (qv) son of Tairdelbach (qv) to retain control of the town in 1126–7. Ragnall (d. 1146), father of Asgall and of his brothers Brótar and Hamund, is styled mórmaer (chief steward) of Dublin (AU) and rí, ‘king’ (Ann. Tig.). This ducal or regnal dignity was inherited by Brótar (d. 1160), probably the eldest brother, and then passed to Asgall. In 1162 Asgall was deposed by Diarmait Mac Murchada (qv), the Uí Chennselaig king of Leinster, who took personal control of the realm of Dublin. When the tide turned against the Leinster overking in 1166, Asgall made submission to the new high-king, Ruaidrí Ua Conchobair (qv), thus becoming one of the agents of Mac Murchada's expulsion, and was duly restored to his realm. The following year he was included among the secular rulers attending the synod at Tlachtga (the Hill of Ward, Co. Meath) as part of the on-going reform of the Irish church.
When Mac Murchada had reasserted his authority with the help of his Anglo-Norman allies, Asgall was confronted with the threat of their combined forces marching on Dublin in September 1170. The Hiberno-Scandinavian nobles pressed Archbishop Lorcán Ua Tuathail (qv) to negotiate on their behalf, but on 21 September the town was stormed and taken by the Anglo-Norman adventurers Miles de Cogan (qv) and Raymond le Gros (Raymond fitz William (qv)), whereupon Asgall made good his escape. On Mac Murchada's sudden death at the beginning of May 1171, the Anglo-Norman earl Strongbow (Richard de Clare (qv)) seized control of Dublin. Asgall immediately returned from the Isle of Man with a seaborne force. Having landed at the Steine near the present College Green, he was captured in a vain attempt to storm the town and was publicly beheaded on or about 16 May 1171. His brother Hamund retained the family lands in north Co. Dublin for some years afterwards.