Need to make wood posts out of metal poles

My next major home project involves replacing a very decrepit wire fence with a new wooden fence. Because of the angle of incline for my yard, I can't use pre-made panels or vinyl fence, so I will need to build it myself. The old fence is attached to metal poles that are set in and filled with concrete. I would like to create wooden boxes to slide over them that will turn them into wooden posts. My question is this... What size lumber should I use to make a box (with butt joints) to slide over a 2" pole?
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