the mother can delay the process by not letting go emotionally - many women who've gone past dates go into labour on their own once an induction or c/s date has been booked - almost signalling that it's *safe* to give birth.
I firmly believe this after DD - I was due on the 30th and because DS was 6 days late I told my Mum not to bother coming down to Melbourne till the 29th. She was very nervous about this and I was fine, the OB said that if it took my body that little bit longer to "bake the baby" LOL that was probably the way I would go again. Every woman is different and some have longer pregnancies than others and different labours etc etc.

Anyway, I went into labour the day Mum was due to come down, and I truly believe it was because I knew she was coming so DS was going to be looked after so it was "safe" to give birth. And I know the first time around I was quite apprehensive and not looking forward to labour at all and the day I did go into labour it was Saturday and DH was home. I wasn't by myself therefore it was "safe".

In terms of stats and graphs, my OB said that 5% of babies come on their due date so that means that 47.5% come between 38 and 40 weeks and the other 47.5% come between 40 and 42 weeks and there would be a peak around the 40th week, giving or taking a few days because the average pregnancy is about 40 weeks, hence the EDD they give you.

As for what triggers labour, I have read they still don't know.