Record promotion is the process of changing the system state of a set of records from the PENDING state to the ACTIVE state. You can set records for promotion manually, using either the Data Steward tools or the Promote batch process.
The Promote batch process also promotes any children associated with the base object that is promoted. If you want to promote children records and grandchildren records, you must run the Promote batch twice. First run the Promote batch job on the parent base object. Then run the Promote batch job again on the grandchild base object.
When you delete records in the MDM Hub, use a similar approach. To delete children records, delete the base object. Then run a second delete job to delete the grandchildren records of the base object.