I found this doodad:
(It's the clippy thing that is shown holding cups onto a line, mouse over the photo for another view). On the package there is a diagram that shows it being used to hold a line around a post. I have set one up in that manner and I am sure it would work for the ridge line of a tarp.
To use it, form a bight at the end of your line (I use a figure 8 on a bight), which can remain permanently.
1) Run the line around a post or tree
2) Attach the doodad to the standing line (the top of the T hangs on the line as shown in the image on the website).
3) Clip the running end into the two semicircular hooks
Now you have an adjustable loop around the post or tree. The two hooks slide over each other to make what is in effect a ring. The T-piece can slide along the line to adjust the tension.
The T-piece is not flat- it is stamped so that the hooks at each end are slightly angled to allow a line to go through almost straight. I don't think it will work with thin lines. I was practicing with some 4mm cord which seemed to be the right size. Load is rated at 120kgf.
Each doodad costs about $5, but I don't know where you'd get one outside the US (I checked REI and Amazon's website).