Letters testamentary are the court-issued document that proves a personal representative has legal authority to act for a deceased person's estate. Banks, title companies, brokerages, and buyers all ask for them - they are the key that unlocks the estate's assets.
In Arizona they are issued when the court appoints the personal representative named in a will. When there is no will, the equivalent document is called letters of administration. Either way, nothing meaningful can happen to estate assets until the letters exist - which is why even simple probates cannot be rushed.
Assets that pass outside probate never need letters at all: trust assets, beneficiary-designated accounts, beneficiary-deed real estate, and survivorship property all move on a death certificate alone.
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Educational information only, not legal advice. Terms have statutory details beyond these summaries - confirm your situation with a licensed professional.