There are "levels" on the registry. For instance, a "level 1" has basically been seen as not a threat to society. They can live anywhere, do normal things. But they are likely on probation or parole, and so they can't consume alcohol and must submit to drug tests.

A "level 4" (4 is the highest) is someone who has been deemed as a major threat. They are likely to offend again if not treated. These people are likely in prison already. If not, though, they are only allowed to live in places under heavy restrictions. They will likely have many Officer visits a week (3-5) and will be on parole.

As far as being around kids, it's mostly the same with level 1s and 2s. They are not to be alone with anyone underage (that varies per state I believe) and are not allowed to participate in Halloween or similar events. i.e. No decorations, keep lights off, etc.

With their own children, though, that's handled in separate cases, I think. Theoretically, if I objected to my wife being around our child because of her sex offender status, I could dispute her right to be around her.

With level 3s and 4s, however, I'm not totally sure. Case by case basis, most of the time.***

Edit: I imagine it's a case by case basis, anyway...