Prefect treats subflow runs similarly to normal flow runs, meaning subflows start as new tasks within the parent flow and there is a full representation of the subflow run in the backend. However, the search did not yield results explicitly mentioning a built-in solution for using a single correlation ID for the entire lifecycle of a run and its subflows.
For detailed and latest information, you may wish to explore the concepts of flows and global coordination within Prefect documentation:
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Composing flows
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Overview - How Prefect Works
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Prefect Global Coordination Plane
If you need to implement something more sophisticated (like a custom correlation ID logic), you might have to extend the given functionality or use additional tooling to track the lifecycle.