One parent can't withhold a child from the other parent in order to punish him or her for not paying child support or doing something the withholding parent didn't like. (m-s-lawyers.com)
The father pays child support for several years, but the mother and child live in a different state from the father / where the birth occurred. (law.stackexchange.com)
The other parent pays child support as a way of contributing to the expenses associated with caring for the child. (silbertfamilylaw.com)