Kobato.

2009 ended 1 season Animation, Drama, Sci-Fi & Fantasy

Kobato is a girl who came to earth to fulfill her wish, which is to go to a certain place. To fulfill that wish, she has to find a bottle and fill it with scarred hearts. Together with her "teacher," which is a stuffed animal, she search for the scarred hearts. However she may not fall in love with any person whom she cures the heart of.