Persons who are in a registrable domestic relationship or a registrable caring relationship may apply to the Registrar, in a form approved by the Registrar, for registration of that relationship if—
(a) one of the persons in the relationship lives in the State; and
(b) each of the persons in the relationship—
(i) is not married or in a registered relationship; and
(ii) is not in another relationship that could be registered under this Part.