After someone passes away who had a trust, trust administration must be completed by the Successor Trustee named in the trust. There is much to do. Generally a Successor Trustee will carry out his or her duties with the help of an experienced estate planning attorney.
Even though there are many duties for the Successor Trustee to carry out (e.g. notice to beneficiaries, manage assets, file tax returns, pay off creditors, etc.), trust administration is less expensive (usually 1/5th the cost of probate) and easier than Probate.