  We calculate the deconfinement line of transitions for large Nc QCD at finite
temperature and chemical potential in two different regimes: weak coupling in
the continuum, and, strong coupling on the lattice, working in the limit where
Nf is of order Nc. In the first regime we extend previous weak-coupling results
from one-loop perturbation theory on S^1 x S^3 to higher temperatures, where
the theory reduces to a matrix model, analogous to that of Gross, Witten, and
Wadia. We obtain the line of transitions that extends from the
temperature-axis, where to a first approximation the transition is higher than
fourth order, to the chemical potential-axis, where the transition is third
order. In the second regime we use the same matrix model to obtain the
deconfinement line of transitions as a function of the coupling strength and mu
/ T to leading order in a strong coupling expansion of lattice QCD with heavy
quarks, extending previous U(Nc) results to SU(Nc). We show that in the case of
zero chemical potential the result obtained for the Polyakov line from QCD on
S^1 x S^3 at weak coupling reproduces the known results from the strong
coupling expansion, under a simple change of parameters, which is valid for
sufficiently low temperatures and chemical potentials.
