  We examine baryonic matter at quark chemical potential of the order of the
confinement scale, $\mu_q\sim \lqcd$. In this regime, quarks are supposed to be
confined but baryons are close to the ``tightly packed limit'' where they
nearly overlap in configuration space. We show that this system will exhibit a
percolation phase transition {\em when varied in the number of colours} $N_c$:
at high $N_c$, large distance correlations at quark level are possible even if
the quarks are essentially confined. At low $N_c$, this does not happen. We
discuss the relevance of this for dense nuclear matter, and argue that our
results suggest a new ``phase transition'', varying $N_c$ at constant $\mu_q$.
