  Statistical hadronization models are extremly succesful in describing
measured ratios of hadrons produced in heavy-ion collisions for a wide range of
beam energies from SIS to RHIC. Using the idea of statistical hadronization at
the phase boundary within the framework of a recently proposed dynamical model
for the thermodynamics of fireballs, we establish a relation between the
equation of state (EoS) in the partonic phase probed at the phase transition
temperature T_C and the measured hadron ratios. In this way, the ratios can be
predicted parameter-free. We demonstrate that this framework gives a consistent
description of conditions both at SPS and RHIC. As the data on dilepton
emission from heavy ion collisions give evidence for strong in-medium
modifications of hadronic properties, we schematically investigate the
sensitivity of our results to such modifications and qualitatively sketch a
consistent scenario involving such in-medium effects.
