[en] Large toroidal and poloidal asymmetries with characteristics which are sensitively dependent on q_a, the vertical position of the plasma, and the type of additional heating are observed in the energy flow to the ASDEX divertor target plates. The largest asymmetries and total energy depositions are observed during lower hybrid wave injection experiments with approximately 50% of the input energy going to the combined divertor targets and shields. A maximum localized energy density loading of 10 MJ/m² is typical under these conditions. Measurements of the asymmetries are consistent with a model in which magnetic islands and ergodicity due to intrinsic magnetic perturbations dominate the energy transport across the primary magnetic separatrix. These results emphasize the essential role of resonant magnetic perturbations in determining the performance of tokamaks and demonstrate that non-axisymmetric effects caused by small perturbations become increasingly important in determining the transport properties as the injected power is increased. 5 refs., 4 figs., 1 tab