This article introduces probabilistic cluster branching processes, a probabili- stic unfolding semantics for untimed Petri nets with no structural or safety assumptions. The unfolding is constructed by local choices on each cluster (conflict closed subnet), while the authorization for cluster actions is governed by a stochastic trace, the policy. The probabilistic model for this semantics yields probability measures for concurrent runs. We introduce and characterize stopping times for this model, and prove a strong Markov property. Particularly adequate probability measures for the choice of step in a cluster, as well as for the policy, are obtained by constructing Markov Fields from suitable marking-dependent Gibbs potentials.