  We study the interplay between the chiral and the deconfinement transitions,
both at high temperature and high quark chemical potential, by a non local
Nambu-Jona Lasinio model with the Polyakov loop in the mean field approximation
and requiring neutrality of the ground state. We consider three forms of the
effective potential of the Polyakov loop: two of them with a fixed
deconfinement scale, cases I and II, and the third one with a $\mu$ dependent
scale, case III. In the cases I and II, at high chemical potential $\mu$ and
low temperature $T$ the main contribution to the free energy is due to the
Z(3)-neutral three-quark states, mimicking the quarkyonic phase of the large
$N_c$ phase diagram. On the other hand in the case III the quarkyonic window is
shrunk to a small region. Finally we comment on the relations of these results
to lattice studies and on possible common prospects. We also briefly comment on
the coexistence of quarkyonic and color superconductive phases.
