This anime is called "Usagi Drop", or as it is translated into English, "Bunny Drop". It started out as a manga series and then got its 15 minutes of fame by not only becoming an anime series last year but it also got its live-action treatment via flavour-of-the-month child actress Mana Ashida and actor Ken'ichi Matsuyama.
Saw the pilot episode and it has that languid feeling with all the pastels, seemingly pencil-drawn animation, and slice-of-life Hayao Miyazaki-like story. The story is about a young feckless man, Daikichi, who has to race back to the family home to participate in the funeral of his grandfather who supposedly left an illegitimate child, Rin, much to the family's horror. After a couple of days of haranguing and bickering about what is to be done with the precocious Rin, an annoyed Daikichi decides to take her in on his own.
Obvious thing to say, but "Usagi Drop"(probably not a few foreign anime fans have snickered about calling it Usagi Droppings instead) is a lot more down-to-earth than "Mawaru Penguindrum". I like them both in their different ways. The opening theme song, "Sweet Drops" is sung by PUFFY, the same female duo who made a splash at the South by Southwest Festival in Austin, Texas over a decade ago (cannot believe it's approaching 20 years since they first debuted), and the ending theme is a pretty nice tune by Kasarinchu called "High, High, High"....almost like a song that The Traveling Wilburys would've tried out. It's featured in the video above.