The bottom boundary layer exerts a powerful control over buoyant coastal currents that contact the bottom, providing a mechanism for trapping density fronts along isobaths. Recent observations suggest that this mechanism may play a role in shelfbreak front dynamics. Here previous studies are extended to investigate frontal trapping by the bottom boundary layer in deeper water typical of shelf breaks and in the presence of ambient stratification. A primitive-equation numerical model is used to study a buoyant current traveling along a vertical wall as it encounters shallow bottom topography typical of a continental shelf. At the initial point of contact, a surface-to-bottom front forms with an associated surface-intensified, geostrophic current. In the absence of bottom friction, the current shoals and continues along the shelf close to the coast. In the presence of bottom friction, buoyancy advection in the bottom boundary layer moves the front offshore (across isobaths) until it reaches a depth where the cross-isobath transport in the boundary layer nearly vanishes. The front remains trapped at this isobath, h∗, which can be estimated theoretically as a solution of The frontal trapping mechanism is remarkably robust, in fact so robust that the presence of a shelf break has little effect on the final location of the front. Bottom stress is necessary for the frontal trapping mechanism, but the trapping isobath is relatively insensitive to the magnitude of the bottom friction coefficient. The near-surface part of the front is sometimes unstable, but it can be stabilized either by ambient stratification or by a weak background current in the direction of the buoyant inflow.