Offline dynamic connectivity: Process edge insertions, then answer "were u and v connected after operation k?"
Rollback operations: Undo union operations by reverting to an earlier version.
Branching histories: Create different "timelines" from the same base state.
Comparison with Link-Cut trees:
- Link-Cut: amortized, supports cut
- Persistent UF: worst case, no cut support, version history
Use persistent UF when you need version queries but not edge deletion.