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−μB-plane. The deviations from the free ideal hadron gas baseline at $\mu_B = 0$ and T≈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 $\mu_B \approx 1.5$ GeV, and at even higher baryon densities $\mu_B \approx 2.4$ GeV, the behavior of fluctuations is controlled by the deconfinement cross-over. The CMF model also describe well the static properties of high μB 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≅0 and high densities, $\mu_B > 1$ GeV.