Graph Neural Networks (GNNs) are the first choice methods for graph machine learning problems thanks to their ability to learn state-of-the-art level representations from graph-structured data. However, centralizing a massive amount of real-world graph data for GNN training is prohibitive due to user-side privacy concerns, regulation restrictions, and commercial competition. Federated Learning is the de-facto standard for collaborative training of machine learning models over many distributed edge devices without the need for centralization. Nevertheless, training graph neural networks in a federated setting is vaguely defined and brings statistical and systems challenges. This work proposes SpreadGNN, a novel multi-task federated training framework capable of operating in the presence of partial labels and absence of a central server for the first time in the literature. We provide convergence guarantees and empirically demonstrate the efficacy of our framework on a variety of non-I.I.D. distributed graph-level molecular property prediction datasets with partial labels. Our results show that SpreadGNN outperforms GNN models trained over a central server-dependent federated learning system, even in constrained topologies.