Large-scale 3D bounding box annotation is crucial for LiDAR object detection but comes at a high cost. Semi-supervised object detection (SSOD) offers promising solutions to leverage unannotated data, but the predominant pseudo-labeling approach requires careful hyperparameter tuning for training on noisy teacher labels. In this work, we propose a Cross-Scan Object Transfer (CSOT) paradigm for LiDAR SSOD. Central to our approach is Hotspot Network, a transformer-based network that predicts possible placement locations for annotated objects in unannotated scans and assigns scores to each location. By leveraging these contextual consistent location predictions, CSOT successfully enables object copy-paste in LiDAR SSOD for the first time. To train object detectors on partially annotated scans generated by CSOT, we adopt a Spatial-Aware classification loss throughout our partial supervision to handle false negative issues caused by treating all unlabeled objects as background. We conduct extensive experiments to verify the efficacy and generality of our method. Compared to other state-of-the-art label-efficient methods used in LiDAR detection, our approach requires the least amount of annotation while achieves the best detectior. Using only 1% of the labeled data on the Waymo dataset, our semi-supervised detector achieves performance on par with the fully supervised baseline. Similarly, on the nuScenes dataset, our semi-supervised CenterPoint reaches 99% of the fully supervised model's detection performance in terms of NDS score, while using just 5% of the labeled data.