Wills on NY divide assets that are owned as of the date of death. A bank account with ITF operates to transfer the asset to the named beneficiary on the date of death by the presentment of the death certificate. It does not pass through the will in NY. The fancy name is a Totten Trust for an ITF account. The same goes for life insurance policies which go to the named beneficiary and does not pass through the will, unless the beneficiary is The Estate of the Decedent. Consult with a local NY lawyer and bring all the documents, will, bank account, life insurance policy, investment accounts and others at the time of e consultation.
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In Trust For (ITF); Paid on Death (POD) ; accounts with named beneficiaries.... all the same animal. They are testamentary substitutes or non-probatable assets. They pass to the beneficiary by "operation of law" on death. They do not pass through the Will. The account would pass to your two other family members and not pursuant to your mother's Will. Your family members need only present proof of death of your mother and the accounts are theirs.
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