The mean field frozen percolation model, introduced by Toth and treated in [Rath, 2009], is a modification of the dynamical Erdos-Renyi random graph model, where large connected components are deleted with a rate proportional to their size. The model exhibits self-organized criticality: as soon as the graph reaches its critical state, it sticks there. Our talk aims to explain this phenomenon and to highlight some unexpected connections to the theory of non-linear PDE.