We analyze recently compiled data on the production of open heavy flavor hadrons and quarkonia in e+e- as well as pp and p-nucleus collisions in terms of the statistical hadronization model. Within this approach the production of open heavy flavor hadrons is well described with parameters deduced from a thermal analysis of light flavor hadron production. In contrast, quarkonium production in such collisions cannot be described in this framework. We point out the relevance of this finding for our understanding of quarkonium production in ultra-relativistic nucleus-nucleus collisions.
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