Parton-hadron–string dynamics (PHSD) transport approach consistently simulates the full evolution of a relativistic heavy ion collision from the initial hard scatterings and string formation through the dynamical deconfinement phase transition to quark gluon plasma (QGP) to the hadronization and to the subsequent interactions in the hadronic phase. The transport theoretical description of quarks and gluons is based on a dynamical quasiparticle model for partons matched to reproduce lattice QCD results in thermodynamic equilibrium. The transition from partonic to hadronic degrees of freedom is described by covariant transition rates for the fusion of quark–antiquark pairs or three quarks (antiquarks). Studying Pb+Pb reactions from 40 to 158 A GeV, we find that at most 40% of the collision energy is stored in the dynamics of the partons. This implies a large fraction of non-partonic, i.e. hadronic or string-like matter, which can be viewed as a hadronic corona; thus, neither hadronic nor purely partonic models can be employed to extract physical conclusions in comparing model results with data. On the other hand, comparing the PHSD results to those of the hadron-string dynamics (HSD) approach without the phase transition to QGP, we observe that the existence of the partonic phase has a sizeable influence on the transverse mass distribution of final kaons due to the repulsive partonic mean fields. Furthermore, we find a significant effect of the QGP on the production of multi-strange antibaryons due to a slightly enhanced pair production in the partonic phase from massive time-like gluon decay and to a more abundant formation of strange antibaryons in the hadronization process.