Section 78A. If real property is divided by sale, mortgage, upon a petition for partition or otherwise after January first and such division has been duly recorded in the registry of deeds, the assessors, at any time before said real property has been advertised for sale for nonpayment of taxes, upon the written request of the owner or mortgagee of any portion thereof, shall apportion said tax, with costs and interest upon the several parcels thereof, in proportion to the value of each, and only the portion of said tax, interest and costs so apportioned upon any such parcel shall continue to be a lien upon it; and the owners or mortgagees shall be liable only for the tax apportioned upon the parcel owned in whole or in part by them respectively. If a tax so apportioned upon any parcel remains unpaid after such a commitment to the collector, it may be recovered in an action of contract or in any other appropriate action, suit or proceeding brought by the collector either in his own name or in the name of the town against said owners and mortgagees. Assessors shall send notice of the request for such apportionment and of the time appointed therefor, by mail, to every person interested in said real property whose address is known to them.