Axiomatization of branching bisimulation for distributions has been established in the setting of a process language with nondeterministic and probabilistic choice in earlier work. Key ingredient to the proof of completeness of the proposed theory is the notion of stability of

processes and the property that every distribution can evolve, within the same equivalence class modulo branching bisimilarity, into a stable distribution. In this talk we focus on a combinatorial approach to this result, replacing the topological machinery used so far.