Many technologies, including dot projectors and lidar systems, benefit greatly from using polarized illumination. However, conventional polarizers and polarizing beam splitters have a fundamental limit of 50% efficiency when converting unpolarized light into one specific polarization. Here, we overcome this restriction and achieve near-complete conversion of unpolarized light to a spatially uniform polarization state over several output directions with our topology-optimized metasurfaces. Our results provide a path toward greatly improving the efficiency of common unpolarized light sources, such as LEDs, for a variety of applications requiring uniformly polarized illumination. Our fabricated metasurface realizes a 70% conversion efficiency, surpassing the aforementioned limit, and achieves a polarization extinction ratio exceeding 20, when characterized with laboratory measurements. We further demonstrate that arbitrary power splitting can be achieved between three or more polarized outputs, offering flexibility in target illumination.