If I'm not mistaken there is only one story of how they got together. There are many stories of how they first met
Kim used to always say that at the 2000 Australian Open her sister Elke wanted to have Lleyton's autograph. So Kim being the great big sis that she is
went and got the autograph from Lleyton..they started to talk and hit it off I suppose
I believe a couple of months later at the Miami tournie they were sort of officially dating.
They've been together ever since. No break ups that I ever heard of.