Which duty involves managing and distributing the deceased's estate?

The duty that involves managing and distributing the deceased's estate is administering the estate, which is best represented by the choice of disposing of the deceased's body. However, it's worth noting that while the disposition of the body is a significant responsibility, it does not encompass the full range of duties related to managing and distributing the estate.

In the context of estate management, administering an estate typically involves identifying and gathering the deceased's assets, paying off debts and taxes, and distributing the remaining assets to the beneficiaries according to the terms of the will or relevant laws if there is no will.

The other options, such as establishing a trust, conducting estate planning, and handling family law matters, relate to different aspects of property and personal rights management but do not directly pertain to the act of managing and distributing the deceased's estate. Each of these areas serves important functions but does not specifically address the duties assigned to the administration of a decedent's estate.