I chanced upon this technique as a bit of experimentation. It ended up working better than I ever could have imagined. I have used it extensively ever since.
This works best with tarps that have grommets in them, but I think many loop types would work.
When I am about to string up your tarp, I will typically bowline one end of my line to tree A, and then proceed to attach the line to tree B with a trucker's hitch, but loose for now. At this point all you have is a slack line between two trees at the right height. Then I lay the ridgeline of the tarp over the slack line, lining up the grommets (loops etc). Then I push a loop of the slack line through the grommet from below. The loop that protrudes above the tarp then gets fed a short stick of greater diameter than the grommet hole. I repeat this for each grommet. At this point I tighten the trucker's hitch to as tight as I can get it. Now the tarp is probably hanging relatively loose, hung over the tight line. But, if you now roll the sticks back and forth within their loops, this tightens up the tarp like pulleys pulling on it. And, this set up doesn't slip.
What you have is a rigid ridgeline that is taking all the tension. Further you have a tarp that is pulled tight but not overstraining the material. Its fully adjustable without fiddling with the ridgeline rope, and doesn't slip. Finally, when it is time to tear down camp, all you need to do is snap the sticks and the tarp is immediately removable. This set up can be torn down in seconds. This was of great advantage during military time, when you would commonly have to tear down camp and have you ruck sack on and marching all in less than 5 minutes.
Hope this is clear enough