The paper introduces a distributed framework, GCBF+, for safe multi-agent control in large-scale environments with obstacles. GCBF+ leverages graph control barrier functions (GCBFs), which are based on control barrier functions (CBFs) and utilize graph structures to enable scalable and generalizable control. The framework is designed to handle a large number of agents using only local information to maintain safety and reach their goal locations. GCBF+ uses graph neural networks (GNNs) to parameterize a candidate GCBF and a distributed control policy, allowing it to directly process LiDAR point clouds for real-world robotic applications. The paper presents a theoretical framework to prove the safety of an arbitrary-sized multi-agent system using a single GCBF. Extensive hardware and numerical experiments on drones demonstrate the effectiveness of GCBF+ compared to other methods, showing improved performance in complex environments with nonlinear agents and increased agent and obstacle counts. The method does not compromise on goal-reaching while achieving high safety rates, addressing a common trade-off in reinforcement learning (RL) methods.The paper introduces a distributed framework, GCBF+, for safe multi-agent control in large-scale environments with obstacles. GCBF+ leverages graph control barrier functions (GCBFs), which are based on control barrier functions (CBFs) and utilize graph structures to enable scalable and generalizable control. The framework is designed to handle a large number of agents using only local information to maintain safety and reach their goal locations. GCBF+ uses graph neural networks (GNNs) to parameterize a candidate GCBF and a distributed control policy, allowing it to directly process LiDAR point clouds for real-world robotic applications. The paper presents a theoretical framework to prove the safety of an arbitrary-sized multi-agent system using a single GCBF. Extensive hardware and numerical experiments on drones demonstrate the effectiveness of GCBF+ compared to other methods, showing improved performance in complex environments with nonlinear agents and increased agent and obstacle counts. The method does not compromise on goal-reaching while achieving high safety rates, addressing a common trade-off in reinforcement learning (RL) methods.