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STORY: The voting referendums in four areas of Ukraine partly-held by Russian forces, that would allow large swathes of the country to be annexed by Russia, have ended.

And Russian state media is saying that the preliminary and partial results are an overwhelming "Yes," for at least 96% of voters.

The polls, long condemned by the Ukrainian government and Western allies as a sham, now set up a possible major escalation in the war.

This was the separatist leader of the Luhansk region, voting earlier on Tuesday (September 27) on Russian state television, saying it's a "historic moment" and that he's voting for a "happy, bright future" for their children and grandchildren.

What happens next is a dire question.

The regions taking part make up about 15% of Ukrainian territory, and the exercise paves the way for Putin to portray any Ukrainian attempt to recapture them as an attack on Russia itself.

Also, just hours before polls closed one, of President Putin's allies issued a stark new prediction, and warning, over the use of nuclear weapons in the conflict: that if Russia did use a nuclear weapon, that NATO would be too afraid to to respond with their own, and that NATO would still not directly enter the war, either.

The comments were made by Russia's former president and now deputy chair of its security council, Dmitry Medvedev.

In a post on Telegram he wrote, quote, "The demagogues across the ocean and in Europe are not going to die in a nuclear apocalypse."

Russian government officials including Medvedev have repeatedly warned that they might use nuclear weapons to defend newly-annexed territory, although this is the first time he's predicted that NATO wouldn't retaliate in this way.

NATO and the U.S. haven't detailed publicly how they would respond to a Russian nuclear attack on Ukraine, but a White House adviser has said Washington spelled out to Moscow "catastrophic consequences."