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Gianne was Lee Adama's estranged fiancée on Caprica.
Soon before the Cylon attack, Gianne informed Adama that she was pregnant with his child. Adama's own issues with his family made the idea of fatherhood apparently frightening, so he "pushed her away and ran." She stormed off because he wouldn't commit, and Adama failed to contact her again before he left on his assignment to the decommissioning ceremony on Galactica.
Before Adama could change his mind, the Twelve Colonies were attacked by the Cylons. Gianne, and Adama's unborn child, are presumed dead.
Months later, Adama's loneliness and depression since the loss of the Blackbird (TRS: "Resurrection Ship, Part II") leads him to a relationship with Shevon. She later realizes that Adama is trying to somehow replace the memory of Gianne with Shevon and her daughter, and rebukes him (TRS: "Black Market").