When you are married or have a registered partnership, custody of the newborn child is taken care of automatically. In all other situations, including having a contract for living together, nothing is settled regarding the custody of the child. It is recommended to discuss custody of the child during the pregnancy. One option is for the father to acknowledge the unborn child. This is done by both parents signing an official document at the City District Office.
We also recommend choosing the last name of the child before he or she is born. For information on these matters we advise you to follow the above link to the website of the city of Amsterdam.