A revocable living trust is administered by its successor trustee, not by a probate court. After the grantor's death the trust becomes irrevocable and files its own income tax return, so it needs its own employer identification number in place of the grantor's Social Security number; a bank asks for that number before it retitles or opens a trust account. The trustee then collects the trust's assets from each institution that holds them, presents the trust document and the death certificate, and distributes under the trust's terms.
The forms here are the paperwork that collection takes: the EIN application, which prepares IRS Form SS-4 for a trust, the letter of instruction addressed to a specific bank, brokerage, or insurer following its published process for a deceased account holder, and the digital assets recovery letter for an online service's deceased user program. The Trust Settlement Plan lays out the administration in order, the Trustee Compensation Calculator applies the state's rule on the trustee's fee, and the Trust Account Opening Guide covers each bank's process for a trust account.