An overlooked property of hadronic models is that they can become supercritical by abruptly transforming the energy stored in the relativistic protons into radiation. Supercriticality manifests itself when the proton density exceeds a critical value. We seek to map the complete parameter space of this behaviour in cases where a source, consisting of relativistic protons, is expanding so adiabatic losses become important. We search those critical values that lead the system to the supercritical regime and are closely related to Gamma Ray Bursts. For this reason we adopt the Relativistic Blast Wave (RBW) model which is thought to describe the production of a GRB after the initial explosion