When people make revocable living trusts to avoid probate, it's common for them to also make what's called a "pour-over will." The will directs that if any property passes through the will at the person's death, it should be transferred to (poured into) the trust, and then distributed to the beneficiaries of the trust.
The goal is to have all the assets distributed under the terms of the trust document. This has several benefits:
As executor, you're responsible for handling the transfer of any assets that pass under the terms of the will. But instead of distributing assets directly to beneficiaries, you must transfer everything to the living trust.
Obviously, if the deceased person set up a revocable living trust to spare his or her family the expense and delay of probate, it would be a shame if a full-blown probate proceeding were necessary. But a pour-over will is just like any other will; unless there's a probate shortcut authorized by state law, the assets that pass through the will must go through probate.
Fortunately, in most cases, not very much property passes through a pour-over will. If the deceased person did a good job of estate planning, all the valuable assets were transferred to the trust before death. Only things of minor value should pass under the terms of the will—which means that the estate may qualify for special "small estate" probate procedures. These processes, usually called "summary probate," are quicker, easier, and less expensive than regular probate. In most states, you can use them for any kind of property except real estate.
Whether it's through regular or summary probate, your responsibility is to get assets into the name of the trust. Then the trustee takes over.
Once the assets are held in the name of the trust, they become the successor trustee's responsibility. The successor trustee's job is like that of the executor, with the crucial difference that the trustee has control only over trust assets. So the trustee will distribute the trust assets following the terms of the trust document.
If the goal of the living trust was simply to avoid probate, the trust may instruct the trustee to distribute everything to the beneficiaries as soon as possible. (No probate is necessary for trust assets.) If, however, trust assets are left to children or young adults, or to someone who just can't be trusted with money, the trust may leave more complicated instructions.
For example, the trustee might be directed to leave a young beneficiary's money in trust until the beneficiary is a certain age, and then dole it out in three chunks over 10 years. It's entirely up to the person who created the trust. This flexibility means that a trustee may have money management responsibilities long after the executor's job is finished.