Probate
Determining the property distribution and claims against the estate of a deceased person, is the job of the court during probate. It's the process where a legal will is checked for validity, and the estate is settled based on its directions.
The probate court grants approval (granting probate) and turns things over to the executor of the will for distribution of property. Sometimes the executor is named in the will, but if not, the court will appoint one.