Personally, I'd never carry the weight of a dedicated 'tarp pole'! I use my trekking poles if there is nothing
I usually carry one or two 20m lengths of 3mm rope/cord or 3/16 braided nylon rope
(mostly used for a ridge line and hanging my food), along with multiple lengths of braided parachute cord, for tie off the corners/sides. I also carry an extra 6 tent stakes
to anchor to, if there are no available trees/roots/large downed branches, or large rocks nearby.
If there is the odd tree around, but not enough(or properly placed), I'll tie of one end of a ridge line to it, either by tossing a rope over an appropriate branch, or using a trekking pole to slide/push a 'loop' up the trunk of a tree, as high as possible and then use either a large branch/pole to use as another point to tie off to and anchor that branch/pole of by using more cord/rope and a couple of tent stakes.
or, I'll use my trekking poles
I usually always
carry a tarp with me, to provide extra 'living space' during inclement weather, or as a sun shade, for cooking. They are great places for a small group to just 'hang out' under.