Sekirei(2004)

Sekirei

Minato Sahashi is a loser who's failed his college placement exams two years running. But just as he's contemplating giving up and moving back in with his mom, a chance encounter changes his life forever! Enter Musubi, a girl who literally falls into Minato's life! Musubi is a Sekirei, a mysterious being caught up in a game in which only one of her kind can be left standing. But in order to be victorious in this contest, she needs to find her fated partner...and guess who fits the bill??

Caught up in a battle he barely understands, can Minato survive the "Sekirei Project" and emerge victorious? Either way, with his buxom new cohort by his side, his life will certainly never be the same!
Together forever. I'll be by your side!

(Source: Yen Press)