  The thermodynamic properties of high temperature and high density QCD-matter
are explored within the Chiral SU(3)-flavor parity-doublet Polyakov-loop
quark-hadron mean-field model, CMF. The quark sector of the CMF model is tuned
to describe the $\mu_B=0$ thermodynamics data of lattice QCD. The resulting
lines of constant physical variables as well as the baryon number
susceptibilities are studied in some detail in the temperature/chemical
potential plane. The CMF model predicts three consecutive transitions, the
nuclear first-order liquid-vapor phase transition, chiral symmetry restoration,
and the cross-over transition to a quark-dominated phase. All three phenomena
are cross-over, for most of the $T-\mu_B$-plane. The deviations from the free
ideal hadron gas baseline at $\mu_B=0$ and $T\approx 100-200$ MeV can be
attributed to remnants of the liquid-vapor first order phase transition in
nuclear matter. The chiral crossing transition determines the baryon
fluctuations at much higher $\mu_B\approx1.5$ GeV, and at even higher baryon
densities $\mu_B\approx2.4$ GeV, the behavior of fluctuations is controlled by
the deconfinement cross-over. The CMF model also describe well the static
properties of high $\mu_B$ neutron stars as well as the new neutron star merger
observations. The effective EoS presented here describes simultaneously lattice
QCD results at $\mu_B=0$, as well as observed physical phenomena (nuclear
matter and neutron star matter) at $T\cong0$ and high densities, $\mu_B>1$ GeV.
