I don't want biological children, but I would be fine raising a partner's child that they had with someone else. In that was I relate with your partner, although in this case I'm female, so the chances of a child actually being mine without my knowing aren't very high :P
My first boyfriend had three children with a woman he didn't live with, and they were fine, but they lived in the same building, just different apartments, and I'm sure that helped. I'm not sure how common it is otherwise, and if the children would move back and forth or stay with one parent and see the other one less often. I can imagine it would be hard if the biological parent who isn't living with the kid did want children and did want to raise them, that they'd be away from them like that.