The public trustee is an office established pursuant to national (and, where applicable, state or territory) statute, to act as a trustee

Trustee

Trustee is a legal term which, in its broadest sense, can refer to any person who holds property, authority, or a position of trust or responsibility for the benefit of another...

, usually where a sum is required to be deposited as security by legislation

Legislation

Legislation is law which has been promulgated by a legislature or other governing body, or the process of making it...

, where courts remove another trustee, or for estate

Estate (law)

An estate is the net worth of a person at any point in time. It is the sum of a person's assets - legal rights, interests and entitlements to property of any kind - less all liabilities at that time. The issue is of special legal significance on a question of bankruptcy and death of the person...

s where either no executor

Executor

An executor, in the broadest sense, is one who carries something out .-Overview:...

 is named by will

Will (law)

A will or testament is a legal declaration by which a person, the testator, names one or more persons to manage his/her estate and provides for the transfer of his/her property at death...

 or the testator

Testator

A testator is a person who has written and executed a last will and testament that is in effect at the time of his/her death. It is any "person who makes a will."-Related terms:...

 elects to name the Public Trustee.
The first Public Trustee is that of New Zealand

New Zealand

New Zealand is an island country in the south-western Pacific Ocean comprising two main landmasses and numerous smaller islands. The country is situated some east of Australia across the Tasman Sea, and roughly south of the Pacific island nations of New Caledonia, Fiji, and Tonga...

; it was proposed by E.C.