  We study the phase diagram of the three-dimensional SU(3)+adjoint Higgs
theory with lattice Monte Carlo simulations. A critical line consisting of a
first order line, a tricritical point and a second order line, divides the
phase diagram into two parts distinguished by <Tr A0^3>=0 and /=0. The location
and the type of the critical line are determined by measuring the condensates
<Tr A0^2> and <Tr A0^3>, and the masses of scalar and vector excitations.
Although in principle there can be different types of broken phases,
corresponding perturbatively to unbroken SU(2)xU(1) or U(1)xU(1) symmetries, we
find that dynamically only the broken phase with SU(2)xU(1)-like properties is
realized. The relation of the phase diagram to 4d finite temperature QCD is
discussed.
