The survey, commissioned by The Times, showed only 29 percent of those polled said they would never want to hold a referendum on partition. "One sooner" after Brexit day on March 29 2019. but within the next decade.
17 percent of people said they would like to say about the "distant future".
In case the poll took place in 2019, right after a Brexit spelled out by Mrs May's agreement, another 48 percent of them said they would like to join in united Ireland.
Ireland would reach 55 percent of the surveyed, including 11 percent of unionists.
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On the other hand, 42 percent said they would prefer to remain part of the UK, while 3 percent said they did not know.
The poll of 1,334 Northern Irish voters was conducted by LucidTalk, a market research company based in Belfast, between November 30 and December 3.
The Netherlands also says support for the second referendum – with 83 percent of nationalists and 27 percent of unionists supporting one.
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The United States want their MPs in Westminster to do.
Despite Arlene Foster saying her party 10 MPs will not support the deal on December 11, one in four unionists, 26 percent, said unionist parties would be wrong to vote down Mrs May's agreement.
And 38 percent of unionists disagreed or strongly disagreed with the DUP tactics.
The stunning poll comes from another survey conducted by YouGov, and only two constituencies in the UK would be back to the Prime Minister's Withdrawal Agreement.
The survey showed only Tory-held Broxbourne and Christchurch supported Mrs May with 30 other constituencies saying they favored no-deal Brexit.
600 seats said remaining in the European Union would be the best outcome for Britain.
Mrs May has today heard of universities, workplaces and 30 ministers of her Cabinet to garner favor ahead of the meaningful vote.