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Mesh parameterization is central to a broad spectrum of applications. In this paper, we present a novel approach to spherical mesh parameterization based on an iterative quadratic solver that is efficiently parallelizable on modern massively parallel architectures. We present an extensive analysis of performance results on both GPU and multicore architectures. We introduce a number of heuristics that exploit various system characteristics of the underlying architectures to speed up the parallel realization of our algorithms. Furthermore, we demonstrate the applicability of our approach to real-time feature detection, mesh decomposition and similarity-based 3D object retrieval. Finally, we offer visual results and a demonstration video.