  Ideally, the Statistical Hadronization Model (SHM) freeze-out curve should
reveal the QCD parton-hadron phase transformation line in the ($T$,$\mu_B$)
plane. We discuss the effects of various final state interaction phenomena,
like baryon-antibaryon annihilation, core-corona effects or QCD critical point
formation, which shift or deform the SHM freezeout curve. In particular, we
present a method to remove the annihilation effects by quantifying them with
the microscopic hadron transport model UrQMD. We further discuss the new
aspects of hadronization that could be associated with the relatively broad
cross-over phase transformation as predicted by lattice-QCD theory at low
$\mu_B$. That opens up the possibility that various observables of
hadronization, e.g. hadron formation or susceptibilities of higher order
(related to grand canonical fluctuations of conserved hadronic charges) may
freeze out at different characteristic temperatures. This puts into question
the concept of a universal \textit{(pseudo-)critical} temperature, as does the
very nature of a cross-over phase transformation.
