Recent research reveals a negative impact of divorce on children's welfare as a consequence of the reduction in monetary and time contributions by the non-custodian parent. When the custody arrangement is sole custody, the variables that link the absent parent to the child are visitations and child support transfers. We explain visitations and child support transfers using a behavioral model of competitive equilibrium in which both variables are the results of competitive allocations realized in a decentralized noncooperative manner. In our framework the mother has control over visitations and the father has control over child support. Estimates of the model are used to simulate the effects of alternative endowment levels on the proportion of time spent with the noncustodial parent and the ex-post parental income distribution. Our results show that a more equal allocation of time with the child, though beneficial to the children, may have a negative effect for the mother's welfare, increasing the income gap between ex-spouses.