How do you update child records using Automation

[Harriswe]

Since the introduction of Automation it is not clear if the old workflow approach still works. Besides workflow is being phased-out. So Is there a way to update the child records when the parent changes using Automation? For example: I am struggling to find how to pass the parent key to a process for updating the child records. Or perhaps that is the wrong approach.

The use-case is a Service Request is reassigned to a different company, consequently the actions relating to the service request should also be reassigned to the new company.

Any examples on Automation and calling processes gratefully received.