In this paper, the unilateral divorce law is modelled through the combination of exclusive rights on the marriage dissolution and alternative compensation rules benefiting to the parent having custody of the children. Their influence are studied both in the short run (probability and efficiency of divorce) and in the long run (selection of marriages). We show that a decrease in the costs of divorce proceedings has by no means commonplace consequences on marriage contracting; particularly when consideration of parents' altruism and child support is introduced, more marriages are contracted when the cost of divorces decreases.