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An administrator to an estate is the person that takes care of the estate of a deceased person in a probate matter. So if A passes away, and B is named as the Administrator by the Court and accepts the responsibility, B is responsible for moving A's assets from out of A's name and into the names of the heirs and beneficiaries to A's estate, either per a Will that A left, or per default state law if A left no Will.
See HERE for the duties and liabilities of an administrator.
NOTE that the position is not mandatory. You can choose to walk away, instead.
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