  We investigate the behavior of light baryon masses in three inequivalent
large-$N_c$ limits: 't~Hooft, QCD$_{{\rm AS}}$ and Corrigan-Ramond. Our
framework is a constituent quark model with relativistic-type kinetic energy,
stringlike confinement and one-gluon-exchange term, thus leading to
well-defined results even for massless quarks. We analytically prove that the
light baryon masses scale as $N_c$, $N_c^2$ and $1$ in the 't~Hooft, QCD$_{{\rm
AS}}$ and Corrigan-Ramond limits respectively. Those results confirm previous
ones obtained by using either diagrammatic methods or constituent approaches,
mostly valid for heavy quarks.
