How do you feel as/or about a single parent when dating?

Perusing internet dating sites lately, I notice an incredible number of single mothers around my age bracket. I have a good friend who got together with a single girl with one child, they now have another and he supports the whole family on his own, as the father of her first is in jail etc. My Question is: How does someones having a child affect your feelings about a potential relationship? Is it an immediate no no? what if you cant deal with the idea but feel you really have a connection? Are you the one in the position with the child? how do you feel about potential partners? I have the greatest respect for my friends willingness to commit, to what to many may seem a burden. I personally haven’t been in a situation where I have had to contemplate it, thats why Im asking this. So its fairly broad and open, please just share your opinions or personal experience. Thanks.