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A key to successfully exploiting data scale is to design flexible models that can be supervised from various heterogeneous data sources produced by different researchers or vendors. To this end, we propose a simple yet powerful paradigm for seamlessly unifying different human pose and shape-related tasks and datasets. Our formulation is centered on the ability -- both at training and test time -- to query any arbitrary point of the human volume, and obtain its estimated location in 3D. We achieve this by learning a continuous neural field of body point localizer functions, each of which is a differently parameterized 3D heatmap-based convolutional point localizer (detector). For generating parametric output, we propose an efficient post-processing step for fitting SMPL-family body models to nonparametric joint and vertex predictions. 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