The Death Star was huge, I'm sure people fucked and made babies on it. I doubt they would just let people leave the Death Star to go raise their kids. That either means kids were just ejected into space, or they were raised on the Death Star.

Given Darth Vader's history with children, it's not unlikely that he just said "fuck them kids" and had them yeeted, but it's funnier to imagine a Death Star Day Care, so imma go with that as my head canon.

Edit: you guys are coming up with some valid counterpoints, but my head canon is still funnier, so I'm sticking with it.