Motivated by the appearance of runaway electrons during disruptions in present and future tokamaks like ITER, we investigate the transport in mixed phase space Hamiltonian systems. That is, we consider the case where both magnetic islands and chaotic (ergodic) regions are present. We are interested in the regime where the remnants of the disintegrated invariant transport barriers (i.e. the outermost invariant curves in an island), the so-called sticky regions, form layers in the phase space acting as partial barriers to transport. We show, based on considerations from chaos theory, that, besides an exponential decay (as described by Rechester and Rosenbluth), a power-law component is present at the same time, but described by an independent effective time-scale. We successfully apply our model in the standard map, the Ullmann-Caldas nontwist map, and in a JOREK simulation of a JET disruption.