  In this paper, we prove a general halfspace theorem for constant mean
curvature surfaces. Under certain hypotheses, we prove that, in an ambient
space M^3, any constant mean curvature H_0 surface on one side of a constant
mean curvature H_0 surface \Sigma_0 is an equidistant surface to \Sigma_0. The
main hypotheses of the theorem are that \Sigma_0 is parabolic and the mean
curvature of the equidistant surfaces to \Sigma_0 evolves in a certain way.
