This paper describes the adaptation of a well-scaling parallel algorithm for computing Morse-Smale segmentations based on path compression to a distributed computational setting. Additionally, we extend the algorithm to efficiently compute connected components in distributed structured and unstructured grids, based either on the connectivity of the underlying mesh or a feature mask. Our implementation is seamlessly integrated with the distributed extension of the Topology ToolKit (TTK), ensuring robust performance and scalability. To demonstrate the practicality and efficiency of our algorithms, we conducted a series of scaling experiments on large-scale datasets, with sizes of up to 4096^3 vertices on up to 64 nodes and 768 cores.