Definitely, only one parent should list the child, answer "whole year", and say no one else supports the child and there is no custody agreement. The other parent ignores the child completely.
However, whether the mother or father should claim the child depends on other facts, like income and eligibility for child tax credits. Usually, the parent who pays more than half the expenses should claim the child because they can also claim head of household. The other parent files as single with no dependent. However, the only way to know for sure which way leads to a bigger refund is to test both parents.)
