The owners of real property constituting a portion of any district may file with the board a petition praying that such real property be excluded and taken from the district. The petition shall describe the property which the petitioners desire to have excluded. The petition shall be acknowledged in the same manner that conveyances of land are required to be acknowledged and be accompanied by a deposit of money sufficient to pay all costs of the exclusion proceedings. The secretary shall publish notice of filing of the petition, which notice shall state the filing of the petition, the prayer of the petitioners and that all interested persons may appear at the office of the board at the time stated in the notice and show cause in writing why the petition should not be granted. The board shall, at the time and place mentioned in the notice or at the time or times at which the hearing may be adjourned, proceed to hear the petition and all objections presented in writing by any person showing cause why the prayer of the petition should not be granted. The filing of the petition shall be deemed and held as an assent by each petitioner to the exclusion from the district of the property mentioned in the petition, or any part thereof. If it deems it not for the best interests of the district that the property mentioned in the petition, or portion thereof, be excluded from the district, the board shall order that the petition be denied; but if it deems it for the best interests of the district that the property mentioned in the petition, or some portion thereof, be excluded from the district, then the board may order the property mentioned in the petition, or some portion thereof, excluded from the district. Upon allowance of the petition, the board shall file a certified copy of the order of the board with the clerk of the court, and upon order of the court the property shall be excluded from the district.