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 μB=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 crossover transition to a quark matter phase. All three phenomena are crossovers, for most of the T-μB plane. The deviations from the free ideal hadron gas baseline at μB=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 μB≈1.5 GeV. At high baryon densities, μB≈2.4 GeV, the behavior of fluctuations is controlled by crossover to quark matter. The CMF model also describe well the static properties of high μB neutron stars as well as recent neutron star merger observations. The effective equation of state presented here describes simultaneously lattice QCD results at μB=0 as well as observed physical phenomena (nuclear matter and neutron star matter) at T≅0 and high densities, μB>1 GeV.