  Combs are a simple caricature of various types of natural branched
structures, which belong to the category of loopless graphs and consist of a
backbone and branches. We study continuous time random walks on combs and
present a generic method to obtain their transport properties. The random walk
along the branches may be biased, and we account for the effect of the branches
by renormalizing the waiting time probability distribution function for the
motion along the backbone. We analyze the overall diffusion properties along
the backbone and find normal diffusion, anomalous diffusion, and stochastic
localization (diffusion failure), respectively, depending on the
characteristics of the continuous time random walk along the branches.
