Companion quests are quests that are unlocked during the course of gameplay, and directly affect the relationships and epilogues of companions in Dragon Age: Origins.
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Alistair's Family, While in Denerim seek out Alistair's sister, Goldanna.
Flemeth's Real Grimoire, Flemeth still holds her true grimoire. Return to Flemeth's Hut, without Morrigan, for a final confrontation.
Leliana's Past, Marjolaine has sent assassins to kill Leliana. Head to Denerim to settle the score for good.
Oghren's Old Flame, Help Oghren win over Felsi, who works at the The Spoiled Princess.
The Sword of the Beresaad, Follow the trail of clues to find the current owner of Sten's sword.
Wynne's Regret, Ask Sarel (with Wynne in your party) about Aneirin, and travel north, just past the Mad Hermit's campsite to find Aneirin.
A Golem's Memories, After A Paragon of Her Kind, talk to Shale to find out where she came from.