On anomalous transport on comb structures

New transport properties of regular comb structures (associated with transport processes at the threshold of percolation and driven by temporally correlated noise) are identified. These include the first realization of transitions from normal diffusion to either anomalous diffusion or to ballistic transport, and the occurrence of super-diffusion. An effective media approximation introduced recently by Arkhincheev (Physica A 307 (2002) 131) is shown to predict accurately transport along the backbones of random comb structures.