After the death of his father Olaf was reared by his grandmother Aud the Deep-minded,[2] and emigrated with her to Iceland, where they settled at the estate called Hvamm in the Laxardal region.
[5] She indeed died during the festivities that lasted 3-days, but the feast was continued to commemorate both Olaf's marriage and Aud's death.
The Landnámabók gives briefer notice on this, merely stating she died during the funeral feast she held for herself in anticipation of her own death.
[3] The children of Olaf and Alfdis were Thord Gellir, Thora, Helga, Thorunn, and Thordis.
Shortly after his death, his nephew Hoskuld Dala-Kollsson named his illegitimate son Olaf the Peacock as namesake[6][7] (Olaf the Peacock had a son Kjartan Óláfsson, who was the beloved of Guðrún Ósvífrsdóttir, heroine of Laxdæla saga).