When a person dies and leaves a will the person or people who have been named as the executor in the will have the job of distributing the estate.
If the deceased did not leave a will their estate is generally distributed by the deceased's closest living relative, this person is called the administrator.
The role of the executor or administrator is to administer the deceased's estate, which includes settling any debts that the deceased has left and distributing the remainder to the beneficiaries named in the will or according to the rules of intestacy.
If the deceased's estate includes land (or an interest in land), or one or more of the financial assets are worth more than $15,000, then probate or letters of administration will have to be obtained.
If these are not required, the executor or administrator will probably need to provide evidence of the death (eg the death certificate), to the organisations holding the funds (eg the bank).