And in addition to the question of priority, is the question of administration: Do these accounts go through Probate? Are they subject to the standard rules and procedures of Trust Administration, or are they handled another way? I realize I am bringing up a lot of questions, but the answers are very simple.
So when it comes time to administer an estate, the financial institutions fulfill their contract by issuing checks or transferring accounts to the designated beneficiaries on the accounts, completely separate from any Probate or Trust Administration proceedings. However, there are three possible outcomes to this situation: 1) the designated beneficiary on the account is alive and well, 2) the designated beneficiary is an existing Living Trust, or 3) there is no designated beneficiary.
First, if the designated beneficiary is alive and well, that beneficiary will work with the financial institution to obtain the funds, or if a life insurance policy, then work to receive the proceeds from the policy. Second, if the designated beneficiary is a Living Trust, then the proceeds will be distributed to the Trust. The Trustee is then able to access the funds to distribute them consistent with the terms of the Trust. Third, if there is no designated beneficiary, the proceeds will be distributed to "The Estate of <The Original Account Owner>, which means that only through a formal Probate process will that be distributed.
In sum, a named beneficiary on an account or life insurance policy will receive the proceeds pursuant to a contract between the original account owner and the financial institution, completely outside of Probate or the Trust Administration process. A Trust named as the beneficiary will receive the proceeds outside of Probate, but such proceeds will need to be distributed pursuant to Trust provisions, and accounts that have no named beneficiaries (and are not otherwise owned by the Trust) will essentially need to go through a formal Probate process.