Methods, apparatus, and systems for distributing network loads in a manner that is resilient to system topology changes. Distribution functions and associated operations are implemented on multiple load splitters such that if a load splitter becomes inoperative, another or other load splitters can forward packets corresponding to flows previously handled by the inoperative load splitter without requiring flow state synchronization to be maintained across load splitters. The distribution functions are implemented in a manner that distributes packets for the same flows to the same servers through system topology changes, addressing both situations when servers fail and/or are taken off-line and when such servers or replacement servers are brought back on-line. The techniques are facilitated, in part, via use of redistributed flow lists and/or Bloom filters that are marked to track redistributed flows. A novel Bloom filter recycle scheme is also disclosed.