What type of wood absorbs the most water?

A dry piece of cut wood, if it is porous enough, may absorb some water by capillary action; it certainly wouldn't do it as efficiently as a sponge. I am assuming that you are talking about living trees taking up water. It is a misconception by some that a cut Christmas tree will absorb water better if the cut end is allowed to dry; this is not true, and in fact dangerous. Wood is not a sponge, and such a tree will be a fire hazard. Trees transport water up and down through the xylem and phloem cells.

The xylem cells are responsible for movement of water upward, and this happens mostly by something called "transpirational pull". The evaporation of water out of the leaves and some other tissues actually causes the water to be 'pulled up' through the system of xylem cells. The transpirational pull is broken if the tissue is allowed to dry out.