Penguindrum

Once you make a decision, does the universe conspire to make it happen? Is destiny a matter of chance, a matter of choice or the complex outcome of thousands of warring strands of fate? All twins Kanba and Shoma Takakura know is that when their terminally ill sister Himari collapses at the aquarium, her death is somehow temporarily reversed by the penguin hat. It's a provisional resurrection, however, and it comes at a price: to keep Himari alive they need to find the mysterious Penguin Drum. In order to do that, they must first find the links to a complex interlocking chain of riddles that has wrapped around their entire existence, and unravel the knots that tie them to a mystifying diary and a baffling string of strangers and semi-acquaintances who all have their own secrets, agendas and "survival strategies." And in order for Himari to live, someone else's chosen destiny will have to change. It's a story of love, fate, life, death… and Penguins!

[from Sentai Filmworks]

Note: Of the 37 chapters serialized, some were merged for the volumes release to end up with 34 chapters.