There are a number of states that have been discussed as wanting to split up due to political and cultural reasons, but we haven't seen this actually happen much. They include...
NE CO/Colorado
Upstate NYS/NYC
South FL/North FL
Southern IL/Chicagoland
Jefferson/California
Northern Cal/Southern Cal
NOVA/Virginia
Austin/Texas
Will we see any of these splits actually occur at any point in our lifetimes? If so, which are most likely?
In 1980, a referendum was held in six counties of Southern New Jersey to secede and form a new state; and it actually passed with 50.90%. It was non-binding, however, and nothing ever came of it (obviously).
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