There is no formal legal recognition or legal rights of 'next of kin'. Certain Acts have given a restricted definition such as the Transplantation and Anatomy Act 1983 (SA) [s 5], which gives a priority as to who makes decisions concerning the donation of organs and tissue, see organ donation. Section 9 of the Burial and Cremation Act 2013 (SA) allows a parent or child of a deceased person to object to cremation, except where the deceased directed he or she be cremated by will or other signed and witnessed document (but a spouse or partner, unless they are also the personal representative - executor of the estate - of the deceased person cannot object).
'Next of kin' are not legally required to provide personal particulars of the deceased relative, but it is helpful if they provide as much detailed information as the funeral director requires. A funeral director can leave the personal particulars with the Registrar of Births, Deaths and Marriages for the purposes of registering the death [Births, Deaths and Marriages Registration Act 1996 (SA) s 38(1)].
Where the deceased has left a will which appoints an executor, it is the executor's responsibility to dispose of the body according to directions in the will, see duties of executors.