The term “administratrix” is most commonly used to refer to the female administrator of an estate. Always restricted to women, the term is generally restricted to legal matters; i.e., the female administrator of an estate is called an administratrix, but the female administrator of a government agency is generally called the administrator. In the United Kingdom, the term may also be applied to the person assigned to administer the affairs of a company in serious financial straits as a prelude — or alternative — to bankruptcy.
In the Western tradition, as well as most others in modern civilization, the goods and other assets a person accumulates during life, including money, become part of his estate upon death, and are distributed or otherwise disposed of in accordance with the deceased's instructions. These instructions are generally left in writing and are typically called the Last Will and Testament, or, more simply, the will. The person writing the will, called the testator, names an executor, usually a good friend or family member. A will's executor is responsible for carrying out its terms, and must do so to the best of his ability, within the limits of the law. If the executor is a woman, she's properly termed the executrix.
When a person dies intestate — that is, without leaving a will — the disposition of the estate generally falls to the courts. In the United States, such cases are usually assigned to special courts called probate courts. The probate judge will delegate that authority to an administrator or administratrix, whose job it is to see to the disposition of the estate's assets, usually in accordance with legally-established standards. It's common for the court, if asked, to assign the job to a surviving family member, especially in the case of a modest estate. Otherwise, the court will assign the job to someone experienced in estate administration, usually a local probate lawyer.
An estate must first pay any legitimate debts owed by the deceased, following which the estate's remaining assets are distributed. To determine the debts, the administratrix will review the deceased's papers, mail, and other correspondence, as well as take steps to inform the community of the death and solicit legitimate claims. Simultaneously, an inventory is taken of the estate and, when appropriate, appraisals made to determine the estate's value. After a reasonable amount of time for creditors to come forward and make claims, the remaining assets are distributed.
An administratrix cannot simply give an estate's assets to those whom she likes or believes deserve them; most jurisdictions in all nations have fairly rigid rules for an estate's disposition. In most cases, assets are liquidated and the funds are distributed among surviving family members according to strict formulas. When there are no surviving relatives, the assets often revert to the government.
Both the executrix of a will and the administratrix of an estate must periodically report to the probate court and document their progress in settling their estates' affairs, and they generally cannot proceed from one phase to another without the court's permission. The distribution of the estate's value to surviving family members is usually the final step in the administration of an estate, and while more modest estates can be disposed of in a matter of weeks or a few months, more complex estates have been known to take a year or longer to clear probate.