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As the perception range of LiDAR increases, LiDAR-based 3D object detection becomes a dominant task in the long-range perception task of autonomous driving. The mainstream 3D object detectors usually build dense feature maps in the network backbone and prediction head. However, the computational and spatial costs on the dense feature map are quadratic to the perception range, which makes them hardly scale up to the long-range setting. To enable efficient long-range LiDAR-based object detection, we build a fully sparse 3D object detector (FSD). The computational and spatial cost of FSD is roughly linear to the number of points and independent of the perception range. FSD is built upon the general sparse voxel encoder and a novel sparse instance recognition (SIR) module. SIR first groups the points into instances and then applies instance-wise feature extraction and prediction. In this way, SIR resolves the issue of center feature missing, which hinders the design of the fully sparse architecture for all center-based or anchor-based detectors. Moreover, SIR avoids the time-consuming neighbor queries in previous point-based methods by grouping points into instances. We conduct extensive experiments on the large-scale Waymo Open Dataset to reveal the working mechanism of FSD, and state-of-the-art performance is reported. To demonstrate the superiority of FSD in long-range detection, we also conduct experiments on Argoverse 2 Dataset, which has a much larger perception range ($200m$) than Waymo Open Dataset ($75m$). On such a large perception range, FSD achieves state-of-the-art performance and is 2.4$\times$ faster than the dense counterpart. Codes will be released at https://github.com/TuSimple/SST.