I use two 11mm dynamic ropes, which have 30% of stretch. I also use four 2" synthetic slings + four 4 1/2 tons shackles for anchor and softeners for the slings to protect against sharp edges. My anchorage is good for 36 000bls. Its over kill, but i know this part wont fail. The shackles are that big just because i wanted a wider bend in my rope vs using carabiners.
The amount of slack in their lines is insane. Unless they have some extra thick ropes (the thickest dynamic ropes i have found is 11mm) or a shock absorber at the top between the anchor and the ropes... you would never see me jump that way. Its pretty much bungee jumping with a little bit of swing at the end, but using climbing ropes..
Myself I started with pulling the ropes fairly tight. Since i got bored after a few jumps, I then started leaving
some slack. so i get a bit of a free fall, but mostly this allows me to do flips when jumping.
On a side note, find a tall bridge near you:
http://www.highestbridges.com/