The aim of these investigations is the description of the power flux on roof-like limiters near the LCFS. Here, the specific subject is the toroidal pump limiter ALT-II of TEXTOR-94. Similar to other plasma facing objects, the surface of ALT-II is shaped to enhance the plasma wetted area; this is achieved by reducing the angle of incidence of the magnetic field to less than 1° for the first 10 mm of the SOL. This small angle of incidence enhances all effects of toroidal non-uniformity as given, for example, by magnetic field ripple. Extensive modelling explains well the observed heating pattern on the limiter surface due to the ripple effect. In contrast to the expectations from density and temperature distributions in the SOL and at the edge of the confined region, an excessive power density is deposited on the first few millimetres near the tip of the limiter roof. Physical effects which could cause this phenomenon are discussed.