A comprehensive model has been developed to study the operating characteristics of high-power high-brightness lasers consisting of a ridge-waveguide section coupled to a tapered region. The model, based on the Beam Propagation Method (BPM), includes a non-linear gain coefficient, current spreading due to junction voltage, and thermal effects taking into account for the first time to our knowledge a longitudinal gradient in the device temperature. We first demonstrate that during operation unwanted radiation that does not couple into the lateral mode of the waveguide, systematically propagates into the tapered region, and leads to the deterioration of the beam quality. To deflect and scatter this radiation, the use of specific cavity-spoiling elements, consisting of grooves etched down through the active region, appears necessary. We also study the role of the ridge section length in the operation of the device. A long ridge-waveguide region, providing both a well defined fundamental mode in the ridge- waveguide, and a gain saturation in the tapered region, improves the beam stability, but can lead, on the other hand, to optical self-focusing. Thermal effects are also investigated. We show how thermal lensing induces a lateral quadratic phase curvature and therefore alters the astigmatism of the device.