Pursuant to this article, after acquiring by purchase, condemnation, or otherwise all outstanding titles, reversions, easements, or other interest in or to the public square, the city in which the public square is located, or if it is not located in a city, the county in which it is located, may erect upon the public square a city hall, county courthouse, or other public building with appurtenances or the city in which the public square is located may grant or lease it to the county in which the city is located for the erection thereon of a county courthouse or other public building.