Modelling of the transport of externally injected methane through a testlimiter exposed to the edge plasma of TEXTOR shows that the observed pattern and low amount of carbon deposition at the limiter can only be simulated when a yield for erosion of re-deposited carbon significantly higher than for graphite together with a low effective sticking probability of hydrocarbons (neutral and ionised CHX) is assumed. Similar assumptions have to be made to reproduce the high amount of carbon deposition observed at the inner louvers in the divertor MkIIa of JET. In contrast to carbon the beryllium transport modelled for JET MkIIa shows no significant deposition at the louvers which is in agreement with the experiment and can be explained by the absence of chemical erosion. Predictive simulations of erosion and re-deposition for ITER have been performed. They show that the maximum net erosion rate at the strike point is less critical than the long-term tritium retention rate, which is estimated to about 6mg/s.