§ 131-f. Streets outside cities. When any territory in a county containing an incorporated city of one hundred thousand inhabitants or upward, lying outside the limits of such city, has been mapped into streets and avenues pursuant to law, the board of supervisors may authorize the establishment of a plan for the grade of such streets and avenues; the alteration of such plan of grades, or of any plan thereof that shall have been established by law; the laying out, opening, grading, constructing, closing and change of line or width, of any one or more of them, and provide for the assessment on property intended to be benefited thereby, and fixing assessment districts therefor, and for the levy, collection and payment of the amount of damages sustained and the charges and expenses incurred, or which may be necessary to incur in carrying out such provisions; the laying out of new or additional streets and avenues upon the established map or plan thereof, the acceptance by town officers of conveyances of lands, for public highways, the naming and changing of names of streets and avenues laid down on said map or plan, and the numbering or renumbering of houses and building lots fronting on such streets and avenues. But such last named power in regard to the alteration of said map or plan, laying out, opening, grading, constructing, closing and change of line, of such streets or avenues, or the numbering or naming thereof, or defraying the expenses thereof, shall only be exercised on the petition of the property owners, who own more than one-half of the frontage on any such street or avenue, or on a certificate of the town board and commissioners of highways of the town, that the same is, in their judgment, proper and necessary for the public interest. If the streets and avenues in respect to which such action is proposed to be taken, shall lie in two or more towns, a like certificate shall be required of the town board and commissioners of highways, of each town. Before making such certificate, such town board, or boards and commissioners of highways, shall give ten days' notice by publication in one of the daily papers of the county, and by conspicuously posting in six public places in each of such towns, of the time and place at which they will meet to consider the same, at which meeting the public, and all persons interested, may appear and be heard in relation thereto. No such street or avenue shall be laid out, opened or constructed, upon or across any lands acquired by the right of eminent domain, and held in fee for depot purposes by any railroad corporation, or upon or across any lands now held by a corporation formed for the purpose of improving the breed of horses, without the consent of such corporations. No town officer shall charge anything for his services under this section, nor shall any charge be made against any such town or the property therein, for the expense of the publication of the notice herein required.