1/8" or 3/16" braided nylon cordage for tie outs. 3/16" is easier to get knots in/out of. don't use a ridgeline for the tarp (Hennessy is built in).
i've also used 7-strand paracord, which is ok, but kinda weird when the outer sheath shifts.
i've also got one corner that's kelty triptease lightline, which, again, is kinda weird when the outer sheath shifts. (i tried doing all 6 tieouts that way once, and didn't like how it lit up like a christmas tree, so i replaced 5 with braided nylon.)