Emigrating with child out of Poland

if a relationship has ended (not married) can one spouse move out of Poland with the child? What would need to happen? since there was marriage and wont be a divorce how to arrange for custody? can a father block a mother from emigrating?

The father is still a father (if named in the birth certificate). All cutody issues are dealt with by family court.
It is possible to stop someone LEGALLY taking kid out of the country.