(a) Ceilings for assessment rolls filed in two thousand three and two thousand four shall only be reduced by one-fourth of the difference between the ceilings or assessments against which taxes were levied on assessment rolls filed in two thousand and the ceilings that would be established for the two thousand three and two thousand four assessment rolls but for the provisions of this section.

(b) Ceilings for assessment rolls filed in two thousand five and two thousand six shall only be reduced by one-half of the difference between the ceilings or assessments against which taxes were levied on assessment rolls filed in two thousand, and the ceilings that would be established for the two thousand five and two thousand six assessment rolls but for the provisions of this section.

(c) Ceilings for assessment rolls filed in two thousand seven and two thousand eight shall only be reduced by three-quarters of the difference between the ceilings or assessments against which taxes were levied on assessment rolls filed in two thousand and the ceilings that would be established for the two thousand seven and two thousand eight assessment rolls but for the provisions of this section.

(d) In calculating the limitations created by this section, the commissioner shall reflect any material change in level of assessment calculated pursuant to article twelve of this chapter and any new construction or demolition in the net amount of five hundred thousand dollars or more in any one year. 2. State assistance shall be paid pursuant to this section, beginning in the year two thousand three, to municipal corporations and special districts that are affected by amendments to this title or title two-B of this article enacted in the year two thousand two; provided that the determination of such assistance shall be subject to the approval of the director of the budget.

(a) Upon issuance of a warrant by a tax-levying body for an assessment roll filed in the year two thousand three, the chief fiscal officer of such tax-levying body shall report to the commissioner the amount of taxes due on any assessment of railroad transportation property appearing on such roll, or the taxes that would have been due on the railroad ceiling for that property if such ceiling were higher than the assessment, and the taxes paid on the same assessment of such railroad real property appearing on the assessment roll filed in the year two thousand. A county shall prepare a single report for the cities, towns, and special districts for which it levies taxes. The commissioner shall thereupon certify to the comptroller payment of state assistance in the amount by which the amount of taxes paid on those assessments or ceilings on the assessment roll filed in the year two thousand exceed the taxes due on the lower of the assessment or ceiling of railroad transportation property appearing on the assessment roll filed in the year two thousand three.

(b) Upon annexation of a warrant to an assessment roll filed in two thousand four through two thousand six, the commissioner shall certify payments in the same amount as those certified for assessment rolls completed in two thousand three. Upon annexation of a warrant to an assessment roll filed in two thousand seven and two thousand eight, the commissioner shall certify payments in the amount of one hundred fifty percent of the amount certified for assessment rolls completed in two thousand three. For assessment rolls completed in two thousand nine through two thousand twelve, the commissioner shall certify payments in the amount of two hundred percent of the amount certified for assessment rolls completed in two thousand three. Any state aid pursuant to this section may be reduced proportionately to reflect an increase in railroad ceilings due to the failure of the owner to receive increased depreciation as provided in section four hundred eighty-nine-g or section four hundred eighty-nine-ii of this article. Such state assistance shall not be available for assessment rolls completed in two thousand thirteen and thereafter.

(c) The amount of any assistance certified pursuant to this section may be modified to reflect proportionally new construction or demolition in the net amount of five hundred thousand dollars or more in any one year.

(d) No payment of state aid shall be made pursuant to this section if a railroad ceiling, adjusted pursuant to paragraph (c) of this subdivision, is higher than the ceiling established for the assessment roll filed in the year two thousand.

(e) No payment of state aid shall be made pursuant to this section if the amount of such payment would be less than one hundred dollars. 3. State assistance shall be paid pursuant to this section to municipal corporations and special districts that are affected by any exemption of railroad real property as a result of acquisition by a public authority, or lease or sublease of such railroad real property by the public authority; provided that such contract for acquisition, or lease or sublease of such railroad real property by the public authority went into effect in the year two thousand three. Such assistance shall be equivalent to the amount the municipality or special district would have received pursuant to subdivision two of this section as if such acquisition, lease or sublease of such railroad real property by such public authority had not occurred.