You can set up a tarp without any trees with lots of different pieces of kit - just think about what you have already and look around at the ground you get to.
If you have a rucksack, pitch the tarp straight over it and I'm sure you will gain enough room to sleep underneath, I've used this before, as well as large rocks, drystone walls, fences, as others have said deadwood. The whole ethos behind a tarp should be flexibility!!
I have carried walking poles before, and if I have them with me then I can create lots of different set ups. I'd argue that although one of the cited reasons some say they choose a tarp is to make it lighter, once you add guy lines, pegs, ridgeline (if carried) possibly a ground sheet of some kind, bivvy bag, mossy net etc. it can soon all add up to the same as a lightweight tent. If you just take a sheet of lightweight material, just big enough to sleep under, use natural cordage and pegs or even the lightest 2mm cord to aid the tarp set up, you could be lighter, but you could soon find yourself carrying enough weight to match a lightweight tent (1kg).
Jay
(Self-diagnosed tarp maniac, tarpologist at heart)