Summary
By Romanian Law, the both parents of a child have parental responsibility automatically. ( art. 98 (1), Family Code)

In case of the divorce, the Court has the obligation to take a decision regarding the minor child custody (art. 42, Family Code).
The divorced parent which has the child custody, has a say in the child’s life, and s/he has certain rights in relation to the child regarding the person and the property of that child.
The divorced parent which has not the child custody, has the right to establish a relationship with the child and has a say regarding to the education, professional training of the child. (art. 43, Family Code) He has not the right to establish the child domicile. The other parent can change the child’s surname or remove the child from the country without consulting the parent that has not the child custody.

However, whether or not a parent has parental responsibility, s/he has an absolute obligation to maintain her/his child financially.

Legal Provisions
Family Code
Article 8 of the European Convention on Human Rights