Abstract
Asymptotic high-energy Koba-Nielsen-Olesen scaling of multiplicity distributions is shown to hold in a class of models. The shape of the scaling function is simply related to the shape of the topological cross sections. A statistical study of the models is made and the thermodynamic limit is investigated. An attempt to relate the impact-parameter picture of high-energy elastic hadron scattering and the scaling phenomenon is presented. Special realistic cases are explored in detail.