Tokyo Godfathers, by Satoshi Kon

Tokyo Godfathers is a 2003 anime movie written by the late Satoshi Kon and Keiko Nobumoto. It's a dramatic comedy (I just can’t bring myself to write "dramedy") about three homeless people who discover an abandoned baby on Christmas Eve, and the convoluted process they go through to return her to her birth parents.

The main characters of Tokyo Godfathers are Gin, Hana, and Miyuki, who’ve formed a semi-family in a tent city within Tokyo. They find a baby within a trash pile, name it Kiyoko, and after convincing Hana--who never knew his own parents and developed the quickest bond with the infant--that there was no way a group of hobos could properly raise a child, they strike out to find who she belongs to and return her (and to find out why she was abandoned in the first place). Along the way, they wind up running into their individual past lives and mulling over the reasons that they became homeless in the first place: Gin and his gambling, which wrecked his family; Hana and his past in a drag bar; and Miyuki’s fight with her parents over her pet cat. There’s also yakuza, foreigners, lottery tickets, lies about maternity, lies in general, falls off tall buildings, and a ton of action.

The film was produced by Madhouse, of Paranoia Agent, Hellsing Ultimate, and FFVII: Last Order (the short found in the super fancy edition of Advent Children) fame. It was distributed in the U.S. by Sony Pictures as a subtitle only release.