Section 11. TRANSFER OF CERTAIN PENDING MATTERS. Except as provided in subdivision thirteen of this section, any matter, application, proceeding or protest undertaken, filed or commenced by, with or before the temporary state housing rent commission or the state rent administrator relating to the regulation and control or residential rents and evictions within a city having a population of one million or more and pending on May first, nineteen hundred sixty-two, shall be transferred to, conducted by, and completed or determined by the city housing rent agency. In discharging such responsibilities the city housing rent agency shall act in conformity with the provisions of the state emergency housing rent control law, and the rules and regulations promulgated thereunder, governing such matters, applications or proceedings, unless at the time such action is taken, such state law, and the rules and regulations promulgated thereunder, have been amended or superseded by local laws, ordinances, rules or regulations adopted pursuant to subdivision five of this section, and in such event, in conformity therewith to the extent such local law, ordinances, rules or regulations are made expressly applicable to such matters, applications or proceedings.