What happens to aborted babies after they die?

The Catholic Church entrusts all children (from the moment of conception) who die without baptism to God’s mercy in hope of their salvation. There is no distinction between children already born and those still in the womb.

"Indeed, the great mercy of God who desires that all men should be saved, and Jesus’ tenderness toward children which caused him to say: ‘Let the children come to me, do not hinder them,’ allow us to hope that there is a way of salvation for children who have died without Baptism" (CCC 1261).