My niece use to work in the maternity ward of one of the local hospitals.

She said mothers on drugs would come in have a baby and leave the hospital without their baby. It happened often enough she asked to be switched to another part of the hospital as it was too heart breaking for her. I asked her what happened to the babies, she supposed someone in the mothers family picked the baby up but wasn't sure.

This was at a fairly small hospital in a smaller town. Have to wonder how often this happens, and are hospitals keeping records of all of this.