 Different kings may have ruled over very different areas and few of them can be seen as exerting any kind of close control over this "far-flung sea kingdom".The Uí Ímair were certainly a powerful force from the late 9th to the early 11th century with dynasts such as Amlaíb Cuarán  and Gofraid mac Arailt claiming kingship of the Isles.Norse sources also list various rulers such as "jarls" Gilli, Sigurd the Stout, Håkon Eiriksson and Thorfinn the Mighty as rulers over the Hebrides who were vassals of the Kings of Norway or Denmark.