Leviathan no Koibito(2007)

Leviathan no Koibito

The year 2077, in a world that has been largely taken over by monsters born out of mutated DNA, live some people who also mutated and became stronger. Follows a girl, Kusaka Yuuki, who's one of these mutants and is technically considered fairly powerful, who "barely defeats" a nameless, immortal boy, names him Tama, and forces him to be her servant, as they fight for a place to call home.

(Source: jCafe24)