A city of the first class, city of the second class, or village may vacate any existing plat and addition to such municipality or such part or parts thereof as such municipality may deem advantageous and best for its interests, and the power hereby granted shall be exercised by such municipality upon the petition of the owner or all the owners of lots or lands in such plat or addition. Such ordinance vacating such plat or addition shall specify whether, and, if any, what public highways, streets, alleys, and public grounds thereof are to be retained by such municipality. Any such ways, streets, and public grounds not retained shall upon such vacation revert to the owner or owners of lots or lands abutting such ways, streets, and public grounds in proportion to the respective ownerships of such lots or grounds. In case of total or partial vacation of such plat or addition, the ordinance providing therefor shall be, at the cost of the owner or owners, certified to the office of the register of deeds and be there recorded by the owner or owners. The register of deeds shall note such total or partial vacation of such plat or addition by writing in plain and legible letters upon such plat or portion thereof so vacated the word vacated, and also make on the same reference to the volume and page in which such ordinance of vacation is recorded, and the owner or owners of the lots and lands in a plat so vacated shall cause the same and the proportionate part of the abutting highway, streets, alleys, and public grounds so vacated to be replatted and numbered by the city surveyor or county surveyor. When such replat so executed is acknowledged by such owner or owners and is recorded in the office of the register of deeds of such county, such property so replatted may be conveyed and assessed by the numbers given in such replat.