Who decided where the US state borders begin and end?

The borders of the original 13 states were defined as colonies by the King of England. Although most of those borders were originally ill-defined and have changed, in some cases significantly, over time. For instance, some of what is now Ohio was claimed by Connecticut, as they believed their land continued west to the Pacific Ocean. This "western reserve", held as payment for their soldiers from the Revolutionary War, is the source of the name of a Cleveland University (Case Western Reserve).

Most of the states are portions of territories bought from other countries (e.g. with France), ceded by other countries by war (e.g. with Mexico), by agreement with other countries (e.g. with British), by agreeement with a state (e.g. Virginia ceding Kentucky and the Northwest Territory - much of the land from what is now Ohio to Minnesota), or by presidential proclamation (by Lincoln and congress with West Virginia).

Many of the states were determined by attempting to break up territories by allocating similar areas (e.g. North and South Dakota; Mississippi and Alabama). Texas largely stayed whole except for the land north of latitude 36 degrees, 30 minutes, enforcing the "Missouri Compromise" which stated that only states south of that latitude could legally have slavery. The only states that stayed whole from the territories from which they were formed are Alaska and Hawaii.