  We present extensive studies on hot and dense quark matter with two light and
one heavy flavors in the Nambu--Jona-Lasinio model with the Polyakov loop
(so-called PNJL model). First we discuss prescription dependence in choosing
the Polyakov loop effective potential and propose a simple and rather sensible
ansatz. We look over quantitative comparison to the lattice measurement to
confirm that the model captures thermodynamic properties correctly. We then
analyze the phase structure with changing the temperature, quark chemical
potential, quark masses, and coupling constants. We particularly investigate
how the effective U_A(1) restoration and the induced vector-channel interaction
at finite density would affect the QCD critical point.
