  We consider three-dimensional lattice SU($N_c$) gauge theories with
multiflavor ($N_f>1$) scalar fields in the adjoint representation. We
investigate their phase diagram, identify the different Higgs phases with their
gauge-symmetry pattern, and determine the nature of the transition lines. In
particular, we study the role played by the quartic scalar potential and by the
gauge-group representation in determining the Higgs phases and the global and
gauge symmetry-breaking patterns characterizing the different transitions. The
general arguments are confirmed by numerical analyses of Monte Carlo results
for two representative models that are expected to have qualitatively different
phase diagrams and Higgs phases. We consider the model with $N_c = 3$, $N_f=2$
and with $N_c=2$, $N_f= 4$. This second case is interesting phenomenologically
to describe some features of cuprate superconductors.
