  We consider two-dimensional lattice SU($N_c$) gauge theories with $N_f$ real
scalar fields transforming in the adjoint representation of the gauge group and
with a global O($N_f$) invariance. Focusing on systems with $N_f\ge 3$, we
study their zero-temperature limit, to understand under which conditions a
continuum limit exists, and to investigate the nature of the associated quantum
field theory. Extending previous analyses, we address the role that the
gauge-group representation and the quartic scalar potential play in determining
the nature of the continuum limit (when it exists). Our results further
corroborate the conjecture that the continuum limit of two-dimensional lattice
gauge models with multiflavor scalar fields, when it exists, is associated with
a $\sigma$ model defined on a symmetric space that has the same global symmetry
as the lattice model.
