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

Light baryon masses in different large-$N_c$ limits