I've posted it before, but here it is again for those who missed it. There would be no UC without Ohio State. They were a political compromise that Rutherford B. Hayes made with the Cincinnati politicians to ensure that Ohio State would be founded, would be located in Columbus away from the agricultural interests and would be a comprehensive Arts & Sciences university--i.e. that Ohio would adopt the singular flagship model of land grand AND A&S in the same university such as Illinois, Wisconsin and Minnesota had already done rather than splitting the roles a'la Indiana or Michigan.
I know that UC uses 1819 as their founding date, but that is highly misleading. In the late 1860s, there were several small private, floundering colleges in Cincinnati with various names, none of which was the "University of Cincinnati." At the same time, Cincinnati was sitting on a fund for which they were looking to find a use. Hayes made a deal with the Cincy politicians that if they supported his goals for Ohio State and the state university system, he would push through a bill allowing municipal universities in cities over 150K in population, which was only Cincinnati at the time. Subsequently, after the founding of Ohio State, the Cincinnati city elders cobbled all these little colleges together (the oldest having been founded in--you guessed it--1819), endowed them with the fund and created the "University of Cincinnati" It was Ohio's first municipal university later to be joined by such similarly illustrious bastions of academia as Toledo, Akron and Youngstown.