Prefetch engines working on distributed memory systems behave independently by analyzing the memory accesses that are addressed to the attached piece of cache. They potentially generate prefetching requests targeted at any other tile on the system that depends on the computed address. This distributed behavior involves several challenges that are not present when the cache is unified. In this paper, we identify, analyze, quantify, and hint on how to face the effects of these challenges, thus paving the way to future research on how to implement prefetching mechanisms at all levels of the cache hierarchy of this kind of system with shared distributed caches.