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Character rigging is universally needed in computer graphics but notoriously laborious. We present a new method, HeterSkinNet, aiming to fully automate such processes and significantly boost productivity. Given a character mesh and skeleton as input, our method builds a heterogeneous graph that treats the mesh vertices and the skeletal bones as nodes of different types and uses graph convolutions to learn their relationships. To tackle the graph heterogeneity, we propose a new graph network convolution operator that transfers information between heterogeneous nodes. The convolution is based on a new distance HollowDist that quantifies the relations between mesh vertices and bones. We show that HeterSkinNet is robust for production characters by providing the ability to incorporate meshes and skeletons with arbitrary topologies and morphologies (e.g., out-of-body bones, disconnected mesh components, etc.). Through exhaustive comparisons, we show that HeterSkinNet outperforms state-of-the-art methods by large margins in terms of rigging accuracy and naturalness. HeterSkinNet provides a solution for effective and robust character rigging.