If I remember correctly, the DC arm of Warner actually has to pay the Cartoon Network to air their shows (similar to how Anime studios have to pay Cartoon Network). It's like a company buying a commercial except that it's a 30 minute block. Cartoon Network is also making money off the additional commercials during the show, but at some point I guess they consider it not with the company's fee.
I think it's the reverse here. The network pays the studio a license fee to produce the series. The studio can invest their own money to increase the show's budget, making back their investment thru selling the show to foreign networks, dvd, & merchandising. Even if the network and studio are corporate siblings, it's handled the same.