We consider a shared store based on distributed shared memory (DSM), supporting persistence by reachability (PBR), a very simple data sharing model for a distributed system. This DSM+PBR model is based on distributed garbage collection (GC). Within a general model for DSM+PBR, we specify a distributed GC algorithm that is efficient and scalable. Its main features are: (i) independent collection of memory subsets (even when replicated), (ii) orthogonal from coherence, (iii) asynchrony, and (iv) a simple heuristic to collect cycles avoiding extra I/O costs. We briefly describe our implementation and show some performance results.