The application of statistical model in heavy ion collisions is discussed in the energy range from SIS/GSI through AGS/BNL up to SPS/CERN and RHIC/BNL. It is shown that in this broad energy range hadronic yields and their ratios resemble a thermal equilibrium population along a unified freeze-out curve determined by the condition of fixed energy per particle \simeq 1GeV. The role of exact conservation of quantum numbers in the kinetic description of rarely produced particles is also analyzed.

PACS numbers: 25.75.Dw