(a) Annually, the assessor shall assess all the taxable property in his county, except state-assessed property, to the persons owning, claiming, possessing, or controlling it on the lien date.
The assessor may assess the property on the secured roll to the person owning, claiming, possessing or controlling it for the ensuing fiscal year.
(b) The assessor may assess all taxable property in his county on the unsecured roll jointly to both the lessee and lessor of such property.
(c) Notices of assessment and tax bills relating to jointly assessed property on the unsecured roll shall be mailed to both the lessee and the lessor at their latest addresses known to the assessor.