If a majority of the votes polled in each of such counties at such election shall be in favor of said proposition, all that territory included within the established boundaries of the petitioning county, shall be united and annexed to the adjoining county, and such petitioning county, shall cease to have any separate existence as a county, but shall be merged into and form an integral part of such adjoining county, in fact and in name, at the time and in the manner hereinafter provided.