Aligning a template to 3D human point clouds is a long-standing problem crucial for tasks like animation, reconstruction, and enabling supervised learning pipelines. Recent data-driven methods leverage predicted surface correspondences; however, they are not robust to varied poses, identities, or noise. In contrast, industrial solutions often rely on expensive manual annotations or multi-view capturing systems. Recently, neural fields have shown promising results. Still, their purely data-driven and extrinsic nature does not incorporate any guidance toward the target surface, often resulting in a trivial misalignment of the template registration. Currently, no method can be considered the standard for 3D Human registration, limiting the scalability of downstream applications. In this work, we propose NSR, a pipeline that, for the first time, generalizes and scales across thousands of shapes and more than ten different data sources. Our essential contribution is NICP, an ICP-style self-supervised task tailored to neural fields. NICP takes a few seconds, is self-supervised, and works out of the box on pre-trained neural fields. We combine it with a localized Neural Field trained on a large MoCap dataset. NSR achieves the state of the art over public benchmarks, and the release of its code and checkpoints will provide the community with a powerful tool useful for many downstream tasks like dataset alignments, cleaning, or asset animation.