They showed up and were registered.
And, not all were allowed entry:
Between 1892 and 1954, more than twelve million immigrants passed through the U.S. immigration portal at Ellis Island, enshrining it as an icon of America's welcome. That story is well known. But Ellis was also a place of detainment and deportation, an often-heartbreaking counterpoint to the joy and relief of coming to America.
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Ellis Island waylaid certain arrivals, including those likely to become public charges, such as unescorted women and children. Women could not leave Ellis Island with a man not related to them. Other detainees included stowaways, alien seamen, anarchists, Bolsheviks, criminals and those judged to be "immoral." Approximately 20 percent of immigrants inspected at Ellis Island were temporarily detained, half for health reasons and half for legal reasons.
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The exclusion of foreign radicals from America was nothing new.
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Soon, Ellis Island's role changed from immigrant depot to detention center. In 1919, as a wave of anti-immigration hysteria swept the country, Frederic C. Howe, Commissioner of the Immigration Service, wrote despondently, "I have become a jailer."
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Further restrictions followed, such as the National Origins Act, which allowed prospective immigrants to be examined in their country of origin, and often refused before making the trip to Ellis Island. Soon after the new law went into effect, Ellis Island "looked like a deserted village," commented one official.
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By the 1930s, Ellis Island was used almost exclusively for detention and deportation.
I could go on and on, but you get the point - Ellis Island was a legal port of entry, one where immigrants came to register themselves and, ultimately, be judged on ability to enter the country. I know, I know, PBS is such a right wing, radical, racist organization that their points have to be made up, but, I looked into it and it really is true.