  During the last years it has become possible to address the cold and dense
regime of QCD directly for sufficiently heavy quarks, where combined strong
coupling and hopping expansions are convergent and a 3d effective theory can be
derived, which allows to control the sign problem either in simulations or by
fully analytic calculations. In this contribution we review the effective
theory and study the $N_c$-dependence of the nuclear liquid gas transition, as
well as the equation of state of baryonic matter in the strong coupling limit.
We find the transition to become more strongly first order with growing $N_c$,
suggesting that in the large $N_c$ limit its critical endpoint moves to high
temperatures to connect with the deconfinement transition. Furthermore, to
leading and next-to-leading order in the strong coupling and hopping
expansions, respectively, the pressure is found to scale as $p\sim N_c$. This
suggests that baryonic and quarkyonic matter might be the same at nuclear
densities. Further work is needed to see whether this result is stable under
gauge corrections.
