Which term captures the legal transfer of assets upon someone's death when no heirs are available?

The term that accurately captures the legal transfer of assets upon someone's death when no heirs are available is escheat. This process occurs when an individual's property or assets transitively revert to the state due to the absence of a legal claimant or heir. Escheat is a principle in law that ensures that property does not remain in a state of limbo and instead is appropriated by the state, which can then manage or allocate it appropriately.

In contrast, probate refers to the legal process of establishing the validity of a deceased person's will and managing their estate, which involves the assets being distributed according to the terms outlined in that will or, if no will exists, according to intestacy laws. Succession pertains to the legal process by which an individual gains rights to inherit assets, typically when there are heirs available to receive the deceased's estate. A trust is a fiduciary arrangement used during a person's lifetime or posthumously to manage assets under specific conditions, but it does not directly address the situation where no heirs exist.

Thus, escheat is specifically tailored to scenarios where there are no claimants or heirs, making it the correct choice for this question.