Background

CGP Grey made a video about this issue.

Ellis Island (and Liberty Island, formerly called “Bedloe’s island”) sits on the New Jersey side of the Hudson River. New York was quite territorial over the river, claiming the entire river as New York territory, such that New York claimed that even New Jersey’s piers belonged in New York’s jurisdiction. New York and New Jersey agreed to a compact in 1834, which set the proper boundary, as one might expect, down the center of the river and bay. The compact also set the other interstate boundaries around Staten Island and into Raritan Bay.

This is the southernmost portion of New York City, which is also the southernmost part of New York City. The New Jersey border is highlighted:

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