  The effect of conserved baryon, isospin and strangeness charges on the
behavior of phase transitions in dense matter is studied. Baryonic matter is
described within the three-flavor Polyakov$-$Nambu$-$Jona-Lasinio model and
several charge fractions $Y_Q$ are considered. The role of the vector
interaction, which can be important to describe dense systems, is discussed.
Special attention is given to the case with charge fraction $Y_Q=0.4$, due to
its importance in heavy-ion collisions and core-collapse supernova matter. It
is shown that the possible formation of chiral-symmetric quark matter in the
laboratory will be favored in asymmetric matter. Besides, the inclusion of the
vector interaction reinforces the formation of quark matter at lower densities.
