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Morrigan is a major companion of the protagonist in Dragon Age: Origins and a supporting character in Dragon Age: Inquisition. She's a Darwinistic witch initially caring for nothing but her survival and gathering more magical power.
Flemeth raised Morrigan isolated from civilization to help Flemeth in her more sinister plans and teach her to be manipulative and look out for herself, proving herself to be a cold and abusive mother.
In Dragon Age: Origins Flemeth commands Morrian to help the Warden in saving Ferelden from the Darkspawn. Morrigan discovers her mother's grimoire and learns that she extends her life by possessing the bodies of her daughters and Morrigan believes she is next. She asks the Warden to kill Flemeth and find her real grimoire so Morrigan can learn how to better protect herself. After the Warden gathers enough armies to fight darkspawn, the final battle gets closer and the Warden learns killing the archdemon means death of whichever Warden kills it. Morrigan reveals Flemeth sent her with the Warden so she could suggest a blood ritual before the final battle. The ritual, which would impregnate Morrigan, would save the Warden from death by diverting the Old God soul from the Warden to Morrigan's unborn child. The Warden can accept or refuse her offer, and either way she will leave, possibly to raise the child in secret.
About two years later, the Warden discovers Morrigan has been researching eluvians and eventually finds and confronts her. Morrigan warns the Warden about Flemeth and refuses to speak of the child if it exists. She leaves alone through the eluvian unless she's in a romance with the Warden, in which case he can go with her.
In Dragon Age: Inquisition, Morrigan is revealed to be the arcane advisor to Empress Celene. If she did the ritual she now has a son Kieran, who has softened her harsh worldview. She joins the Inquisition as an advisor to help in defeating Corypheus, as she believes he seeks an eluvian located in the Temple of Mythal. It turns out Corypheus is not after the eluvian but instead the Well of Sorrows, which contains a millennia of knowledge from Mythal's servants and which apparently binds anyone who drinks from it to Mythal's will. To keep it from Corypheus, either she or the Inquisitor drink from it. Later she and the Inquisitor encounter Flemeth and learn that she's Mythal. Morrigan believes Flemeth wants to possess her body, or Kieran's, but Flemeth merely takes the Old God soul from Kieran without harming him or, if he doesn't exist, does nothing at all. If Morrigan drank from the Well, she learns how to turn into a dragon and uses this form to fight Corypheus' own dragon during the final battle. After Corypheus' defeat she leaves the Inquisition and travels to some place unknown.