It's nothing to do with working, or having a new partner come to that.
If going through a government body the non resident parent should contribute a percentage of their wages (think the basic amount is 15% of a weeks wage for one child). It also takes into account how much the non resident parent has the child, so if is a 50/50 split then no they will not need to pay child support.
Child support usually continues until the child has finished their education, A� levels not Uni.