In 1665, the Duke of York paid off a gambling debt by awarding New Jersey to his drinking buddy George Carteret (who was from Jersey in the Channel Islands). The Duke retained, however, control of "all offshore islands" according to his patent. These included Martha's Vineyard, Nantucket, Block Island, Fisher's Island, Plum Island, Gardiner's Island, Shelter Island, Robbin's Island, Long Island, and all the islands in New York Harbor.
Although New Jersey tried to claim Staten Island, nestled within yards of its shore, a Royal Commission unsurprisingly upheld the claims of the future king. The same went for the little specks of land later called Black Tom Island, Bedloe's Island, Governor's Island, and Ellis Island. Throughout their history, the small islands were owned by New Yorkers. They were only intermittently settled, being used mostly as pasturelands.
During this period, the Bedloe's Island property was sold to the City of New York for use as a quarantine station.
In 1783, with the end of the Revolutionary War, surveyors tried to settle the New York/New Jersey boundary by drawing a straight (if utterly imaginary) line down the center of the Hudson River. Although the line squiggled to include Staten Island in New York, the surveys overlooked Bedloe's Island and Ellis Island both, which ended up on the New Jersey side of the line. Still, the only access to either was by ferry from New York City, they remained owned by either New York City or individual New Yorkers, and everybody just sort of assumed they were New York territory.
However, with the opening of the Statue of Liberty in 1886, the border dispute heated up. Both New Jersey and New York claimed bragging rights over Bedloe's Island. New York wanted a ferry monopoly in New York Harbor. Both States wanted the tax and tourism dollars to be had from the Statue. Although, in the strictest sense, Bedloe's Island was (and is) Federal territory, both States claimed rights to the island. This dispute only grew hotter after Ellis Island became a Federal Immigration Station.
Over time, Jersey City, New Jersey and the State of New Jersey both brought suit against New York for control of the islands, suits which the Federal Government dismissed in favor of New York on an historical basis. It chided both States that Bedloe's and Ellis Islands were now Federal islands anyway, but that did not stop the bragging rights/tourism/tax dollar war, which only got worse when the Federal government began paying New York to maintain utility services to the islands.
Still, the question of "Who Owns Liberty Island?" remained a kind of joke, a kind of squabble, and a kind of jurisdictional black hole for nearly 100 years. It began to erupt again in the 1970s as the Statue of Liberty Centennial approached:
Both States issued "Statue of Liberty" license plates and other commemoratives.
During the run-up to the Centennial, when New Jersey Governor Thomas Kean announced a "New Jersey, The Home of Immigration" campaign, Governor Mario Cuomo of New York torpedoed it in the Press by saying sourly that his ancestors hadn't risked life and limb to come from the Old Country just so they could set foot in, eh, New Jersey. Kean dropped his idea.
The U.S. Supreme Court finally resolved the matter by awarding Liberty Island to New York in 1998.
Electrical power and mail service to Ellis and Liberty Islands is provided by New York, and water and sewage service by New Jersey.
All in all, New Jersey did not come out of this smelling like a rose. But if you've ever been through north Jersey, well, that's nothing new.