Let G be an arbitrary group. The projective complete cohomological dimension of G, denoted by pccd G, is the least integer n for which Hi(G,−)≈H^i(G,−) for i>n, where H^i(G,−) is the complete cohomology of G. We study the properties of projective complete cohomological dimension of a group and then, using these, we give partial answers to three conjectures formulated by Ikenaga, Kropholler, and Talelli.