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3D point cloud semantic segmentation is fundamental for autonomous driving. Most approaches in the literature neglect an important aspect, i.e., how to deal with domain shift when handling dynamic scenes. This can significantly hinder the navigation capabilities of self-driving vehicles. This paper advances the state of the art in this research field. Our first contribution consists in analysing a new unexplored scenario in point cloud segmentation, namely Source-Free Online Unsupervised Domain Adaptation (SF-OUDA). We experimentally show that state-of-the-art methods have a rather limited ability to adapt pre-trained deep network models to unseen domains in an online manner. Our second contribution is an approach that relies on adaptive self-training and geometric-feature propagation to adapt a pre-trained source model online without requiring either source data or target labels. Our third contribution is to study SF-OUDA in a challenging setup where source data is synthetic and target data is point clouds captured in the real world. We use the recent SynLiDAR dataset as a synthetic source and introduce two new synthetic (source) datasets, which can stimulate future synthetic-to-real autonomous driving research. Our experiments show the effectiveness of our segmentation approach on thousands of real-world point clouds. Code and synthetic datasets are available at https://github.com/saltoricristiano/gipso-sfouda.