  We perform a systematic comparison of the statistical model parametrization
of hadron abundances measured in high energy pp, AA and e+e- collisions. The
basic aim of the study is to test if the quality of the description depends on
the nature of the collision process. In particular, we want to see if nuclear
collisions, with multiple initial interactions, lead to "more thermal" average
multiplicities than elementary pp collisions or e+e- annihilation. Such a
comparison is meaningful only if it is based on data for the same or similar
hadronic species and if the analyzed data has quantitatively similar errors.
When these requirements are maintained, the quality of the statistical model
description is found to be the same for the different initial collision
configurations.
