Although what often happens is that now divisions compete against either in suboptimal ways. Search and Maps are separate? Great, until Search decides maps are really cool and starts building their own version, again. It takes a strong hand at the top to prevent division heads from viewing their peers as rivals.
I'm pretty sure Search and Maps will still be operating under the Google organization. They're just spinning off their more "wacky" projects that aren't directly related to Internet technology.