  The phase transition of hadronic to quark matter at high baryon and isospin
density is analyzed. Relativistic mean field models are used to describe
hadronic matter, and the MIT bag model is adopted for quark matter. The
boundaries of the mixed phase and the related critical points for symmetric and
asymmetric matter are obtained. Due to the different symmetry term in the two
phases, isospin effects appear to be rather significant. With increasing
isospin asymmetry the binodal transition line of the (T,\rho_B) diagram is
lowered to a region accessible through heavy ion collisions in the energy range
of the new planned facilities, e.g. the FAIR/NICA projects. Some observable
effects are suggested, in particular an "Isospin Distillation" mechanism with a
more isospin asymmetric quark phase, to be seen in charged meson yield ratios,
and an onset of quark number scaling of the meson/baryon elliptic flows. The
presented isospin effects on the mixed phase appear to be robust with respect
to even large variations of the poorly known symmetry term at high baryon
density in the hadron phase. The dependence of the results on a suitable
treatment of isospin contributions in effective QCD Lagrangian approaches, at
the level of explicit isovector parts and/or quark condensates, is finally
discussed.
