  The grand-canonical version of the thermal model is used to analyze the
ratios of particle abundances measured in ultra-relativistic heavy-ion
collisions. Exactly the same model is applied to study the heavy-ion reactions
at BNL AGS, CERN SPS, and BNL RHIC. A very good description is achieved for
Pb+Pb collisions at SPS, and for Au+Au collisions at RHIC. In these two cases
the value of the temperature characterizing the chemical freeze-out is
practically same: T=168 MeV at SPS and T=165 MeV at RHIC. On the other hand,
the particle ratios measured in the collisions of lighter nuclei are described
only in the qualitative way. We discuss also the effect of the possible
in-medium modifications of hadron masses and widths on the thermal fits. For
Pb+Pb collisions at SPS and Au+Au collisions at RHIC we find that the chi^2
fits favor slightly a moderate (20%) decrease of the masses. In-medium
modifications of the widths have little effect on the fits, unless they are
increased by a factor larger than 2. We study in detail the thermodynamic
conditions characterizing the chemical freeze-out. In particular, we find that
the average baryon energy is 1.6 GeV and the average meson energy is 0.9 GeV.
This difference reflects a different behavior of the mass spectra of mesons and
baryons.
