  The phase diagram is investigated for SU(2) lattice gauge theory in d=3,
coupled to adjoint scalars. For small values of the quartic scalar coupling,
lambda, the transition separating Higgs and confinement phases is found to be
first-order, in agreement with earlier work by Nadkarni. The surface of
second-order transitions conjectured by Nadkarni, however, is shown instead to
correspond to crossover behaviour. This conclusion is based on a finite size
analysis of the scalar mass and susceptibility. The nature of the phase
transition at the termination of first-order behaviour is investigated and we
find evidence for a critical point at which the scalar mass vanishes. The
photon mass and confining string tension are measured and are found to be
negligibly small in the Higgs phase. This is correlated with the very small
density of magnetic monopoles in the Higgs phase. The string tension and photon
mass rise rapidly as the crossover is traversed towards the symmetric phase.
