N.J. Stat. § 54:4-63.2
When any parcel of real property has been sold by any municipality as not needed for public use, and the deed has been delivered after October 1 in any year and before January 1 following, or when any parcel of real property contains any building or other structure which has been erected, added to or improved after October 1 in any year and completed before January 1 following, the assessor shall, after examination and inquiry, determine the taxable value of such parcel of real property as of the first day of the month following completion or sale of said property and if such parcel of real estate was not assessed as of October 1 preceding or if such value so determined exceeds the assessment made as of October 1 preceding, the assessor, shall enter the amount of such assessment or such excess, as an assessment or an added assessment against such parcel of real property, for the subsequent tax year in a list to be known as the "Added Assessment List, 19 . . . " (inserting the name of the year in which the assessment is made); such entry to be made opposite the name of the owner and the description and area of the parcel of real property. In addition, the assessor shall enter in such added assessment list an assessment for that portion of the pretax year between the first day of the month following completion or sale of said property and December 31 to be determined by multiplying the amount of such assessment or such excess by the number of whole months remaining in the pretax year after the completion or sale of said property, and by dividing the result by 12.
N.J.S. § 54:4-63.2