It is called Delivery Man and stars Vince Vaughn. Scheduled to come out in November. This has to be one of the most bizarre ideas for a movie ever conceived(pun intended).
From IMDB: An affable underachiever finds out he's fathered 533 children through anonymous donations to a fertility clinic 20 years ago. Now he must decide whether or not to come forward when 142 of them file a lawsuit to reveal his identity.
It sounds like it was based on the documentary, "Donor Unknown". Young woman wanted to find her genetic father and has his bank number, "150." She tracks down a bunch of half-siblings (the PBS website mentions 14) and the man ends up coming forward. He's a free spirit in Venice, California.
IIRC, there was some shenanigans by the bank, like people had requested that the 'donor' not be used for more than X other people, but I may be conflating another story.
