(a) No household goods carrier, as defined in Section 5109, shall engage in any interstate or foreign transportation of property for compensation by motor vehicle, and no motor carrier shall engage in any interstate or foreign transportation of passengers for compensation by motor vehicle, on any public highway in this state without first having registered the operation with the commission or the carrier’s base registration state, if other than California, as determined in accordance with final regulations issued by the Interstate Commerce Commission pursuant to the Intermodal Surface Transportation Efficiency Act of 1991 (49 U.S.C. Sec. 11506). To register with the commission, carriers specified in this section shall comply with the following:

1. (1) When the operation requires authority from the Interstate Commerce Commission under the Interstate Commerce Act, or authority from another federal regulatory agency, a copy of that authority shall be filed with the initial application for registration. A copy of any additions or amendments to the authority shall be filed with the commission.
2. (2) If the operation does not require authority from the Interstate Commerce Commission under the Interstate Commerce Act, or authority from another federal regulatory agency, an affidavit of that exempt status shall be filed with the application for registration.
3. (3) The commission shall grant registration upon the filing of the application pursuant to applicable law and the payment of any applicable fees, subject to the carrier’s compliance with this chapter.