Here in WI, percentage of time spent in each house is a consideration, along with income.
There is usually some child support paid by one party to another, but it's not necessarily a lot in a joint custody (called shared placement here) situation.
My partner has his daughter about 40% of the time, which is considered shared placement (anything over 25% for both parties is), and he pays around a token amount per month for CS. He'd pay much more if he didn't have shared placement, but if his ex started making a lot more money, she might end up paying him even though he has less time.
ProtoLawyer (the now-actual lawyer, this isn't legal advice, please don't take legal advice from some anonymous yahoo on the Internet)
Spouse (the political geek) * Stepdaughter (the artist) * and introducing...the Baby (um, he's a baby? He likes shiny things).