Rutgers University
Rutgers University was founded in 1766 as Queen's College also by Royal Charter, but by the grandson of George II, King George III (also known as "that dude who taxed Americans without representation and later made a habit of talking to trees").
Today, Rutgers is the official State University of New Jersey, a designation that encroached upon it with the awarding of a land grant in 1864 of 210,000 acres in, of all places, Utah (amidst feverish competition with Princeton, no less)[1]. By 1945, Rutgers had officially been designated a state university.
Rutgers sometimes tries to get cute by claiming it was "invited to join the Ivy League". Which is preposterous, as the Ivy League (an organisation open only to private schools) was not founded until 1954, well after Rutgers was designated a public university.
Rutgers also tries to claim that it is a "sister school" of Columbia, since its original namesake was "Queen's" rather than "King's". However, the "Queen" for whom Rutgers is allegedly named is Charlotte of Mecklenburg-Strelitz, who was not George III's sister, but rather his consort. Ergo, a more proper designation for Rutgers would be "Columbia's bitch", a fact that will no doubt spurt an obligatory Barnard joke.
Nonetheless, ties between Columbia and Rutgers were, at one point in the past, somewhat strong. An entire class of Columbia juniors in the early 19th century threatened to withdraw and petition for admission as a class to Rutgers when the Trustees were considering expelling a particularly troublesome member. And supposedly, there were once "annual Queen's College-King's College (Columbia) debates"[2], but no one's heard of one on recent memory.