Tokyo Godfathers. Unfortunately, I haven't seen it yet myself but the premise is such, according to Wikipedia:
One Christmas Eve in present day Tokyo, three homeless people — Gin (ギン?), a middle-aged alcoholic, Hana (ハナ?), a transwoman and former drag queen, and Miyuki (ミユキ?), a runaway girl — discover an abandoned newborn while searching in some trash. Deposited with the unnamed baby is a note asking the finder to take good care of her and a bag containing clues to the parent's identity. The trio sets out to find the baby's parents. The baby is named Kiyoko, "pure child" as she is born on Christmas Eve.