every one is different, I would assume a normal person would towards the last 10 weeks. I become fully dialated at 5 months, but that's me....and I never have made it past 8 1/2 months... But like I said, everyone is different, some dialate, some don't until their water breaks
Towards the end. You can start dilating a couple months before the due date or not until the last couple days. I was dilated to a 1 for like 2 months and my friend was at a 2 for about a month and then ended up going a week late. My mom however wasn't even dilated and then within a couple hours was fully dilated when she went into labor. It all just depends on your body.