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Family name Ásbjörn (Ásbjörn ) , in the entire world, is an extremely rare cognomen. Much more prevalently, Ásbjörn is the forename as well as the last name.
Jónsson, Björgvinsson, Skarphéðinsson, Sigurpálsson, Jóhannesson, Stefánsson, Þorleifsson, Ásbjörnsson, Þorsteinsson, Einarsson, Gíslason, Björnsson, Arnarsson, Árnason, Eðvaldsson, Ólafsson, and Sveinbjörnsson