Erdos-Renyi random graphs + forest fires = self-organized criticality
  We modify the usual Erdos-Renyi random graph evolution by letting connected clusters 'burn down' (i.e. fall apart to disconnected single sites) due to a Poisson flow of lightnings. In a range of the intensity of rate of lightnings the system sticks to a permanent critical state. 
Balazs Rath (TU Budapest, Institute of Mathematics), Balint Toth (TU   Budapest, Institute of Mathematics)