Some 49% of people in Northern Ireland would vote to remain in the UK with 43% opting for Irish unity if a border poll was held now, a new opinion poll shows.
Eight per cent of people here were undecided in the LucidTalk opinion poll for BBC Spotlight.
In the Republic, where polling was carried out by Ireland Thinks, 51% of people said they would vote for Irish unity with 27% supporting Northern Ireland remaining in the UK, and 22% undecided.
DUP leader Arlene Foster told Spotlight's special programme on the centenary that a referendum on the constitutional way forward should not be on the agenda.
"We shouldn't even be talking about a border poll. We should be talking about why it's important to be within the UK, why it's the right thing for all our people," she said.
"Why in heaven's name would people give that up to go in with a small state (to) a huge EU when you could be part of an integrated UK which is a global player?"
Mrs Foster said she was confident Northern Ireland would remain part of the UK long after she had passed away because it was a "rational political ideal".
In the LucidTalk poll, 55% of people in Northern Ireland thought the Union would still be in place in 10 years' time while 32% believed it wouldn't.
In the South, 59% thought the constitutional status quo would remain while 26% did not.
But when asked if Northern Ireland would be part of the UK in 25 years' time, a majority on both sides of the border said it wouldn't.
A total of 51% of people here thought the Union would have ended with 37% believing it would still exist. In the South, 54% thought there would be a united Ireland and 26% said Northern Ireland would still be part of the UK.
More than three-quarters (76%) of people here thought that violence could return to Northern Ireland with 87% of people in the Republic also sharing that view.
A total of 48% of people here wanted the protocol scrapped with 46% saying it should be retained. In the South, 74% thought it should be kept and 10% wanted it axed.
Only 40% of people here saw Northern Ireland's centenary as a cause for celebration.
A total of 45% disagreed with the proposition that "the formation of Northern Ireland 100 years ago was an achievement which should be celebrated".
Almost half of respondents (48%) agreed with the statement that "the partition of Ireland and the creation of a land border 100 years ago was a negative development which should be regretted".
Exactly half of those questioned wanted to concentrate on current challenges such as the Covid-19 rather than the centenary.
Six in 10 backed marking Northern Ireland's formation in a neutral manner acknowledging different opinions on the subject.
In the Republic of Ireland, celebrating the centenary was even more unpopular, with just 12% agreeing with the proposition.
A total of 71% of those questioned in the South expressed regret over partition.
Polling in Northern Ireland was carried out from April 5 to 7 and in the Republic from April 6 to 9.