What does "Probate Administration" mean?
It means processing the affairs of a decedent. It may be through a will, or not. There may be land and/or trusts involved. It could be insolvent; some have it that way on purpose.
Probate administration is the process of dealing with the System in the event of a death. It will always be as long as there is some kind of government and civilization. People need help with that.