We present 3D-MPA, a method for instance segmentation on 3D point clouds. Given an input point cloud, we propose an object-centric approach where each point votes for its object center. We sample object proposals from the predicted object centers. Then, we learn proposal features from grouped point features that voted for the same object center. A graph convolutional network introduces inter-proposal relations, providing higher-level feature learning in addition to the lower-level point features. Each proposal comprises a semantic label, a set of associated points over which we define a foreground-background mask, an objectness score and aggregation features. Previous works usually perform non-maximum-suppression (NMS) over proposals to obtain the final object detections or semantic instances. However, NMS can discard potentially correct predictions. Instead, our approach keeps all proposals and groups them together based on the learned aggregation features. We show that grouping proposals improves over NMS and outperforms previous state-of-the-art methods on the tasks of 3D object detection and semantic instance segmentation on the ScanNetV2 benchmark and the S3DIS dataset.