Identifcation and ftting is an important task in reverse engineering and virtual/augmented reality. Compared to the traditional approaches, carrying out such tasks with a deep learning-based method have much room to exploit. This paper presents SMA-Net (Spatial Merge Attention Network), a novel deep learning-based end-to-end bottom-up architecture, specifcally focused on fast identifcation and ftting of CAD models from point clouds. The network is composed of three parts whose strengths are clearly highlighted: voxel-based multi-resolution feature extractor, spatial merge attention mechanism and multi-task head. It is trained with both virtually-generated point clouds and as-scanned ones created from multiple instances of CAD models, themselves obtained with randomly generated parameter values. Using this data generation pipeline, the proposed approach is validated on two diferent data sets that have been made publicly available: robot data set for Industry 4.0 applications, and furniture data set for virtual/augmented reality. Experiments show that this reconstruction strategy achieves compelling and accurate results in a very high speed, and that it is very robust on real data obtained for instance by laser scanner and Kinect.