The Hudson River separates Manhattan from New Jersey. The East River separates Manhattan from Brooklyn and Queens while the Harlem River separates the Bronx from Manhattan.
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Since a U.S. Supreme Court ruling in 1998, Ellis Island, which is federal property, belongs within the territorial jurisdiction of both New York and New Jersey depending upon where you are.
Even though Ellis Island and Bedloe's Island (now Liberty Island) are totally within New Jersey, the two States agreed that New York would retain exclusive jurisdiction of both Islands as they existed at that time. The agreement was signed by commissioners from both states and approved by the U.S. Congress.