The survey revealed more than 60 percent of those living in the north, and more than 80 percent of those living south of the border would like the process to be scrapped if an agreement was reached between Britain and the EU which meant a tough limit.
The survey, joint mission of RTE and BBC Northern Ireland, also showed that 62 percent of those living in Northern Ireland believed that a united Ireland was more likely as a result of Brexit.
The figure was significantly higher than in the Republic, where the figure was 35 percent.
When Brexit speaks when the playoffs, the two TV networks cooperated for a special live Brexit program on Monday night.
Attitudes about Brexit and its effect on humans on both sides of the border were investigated.
RTE's Claire Byrne and BBC's Stephen Nolan switched studios, with Byrne broadcast from BBC Northern Ireland in Belfast and Mr. Nolan comes from RTE studio in Dublin, both in front of live audiences.
In Belfast, Fin Gael Senator Neale Richmond, journalist Susan McKay and Ben Lowry from Belfast News Letter went to Ms Byrne.
In Dublin, member Nolan was united with the leader of traditional Unionist Voice Jim Allister, Sinn Fein's David Cullinane, Alliance Party leader Naomi Long and Conservative MP Chris Chope.
Asked how they thought Brexit would affect their own financial situation, in Northern Ireland said 55 percent believed they would get worse, while only nine percent said they believed they would get better and 30 percent said it would not do any difference.
In the Republic, 34 per cent thought they would be worse, with two per cent believing they would be better and almost half said it would not make any difference.
The survey was conducted by Amarach Research in the Republic and LucidTalk in Northern Ireland.
More than 2,000 people were interviewed over the island last week.
The issue of arrangements for the Irish border is central to the Brexit debate.
Brexiteers has accused the EU and the Irish government to focus on the issue as a tactic aimed at getting leverage by Prime Minister Theresa May.
Others have suggested, however, that Britain glosses over the problem at its risk.
In October, Taoiseach of Ireland or Prime Minister Leo Varadkar spoke of a "very right" risk of returning to the dark days of Troubles in Northern Ireland if a hard border returns.
He added: "I just wanted to make sure there was no sense in space that somehow in Ireland or in the Irish government exaggerated the real risk of returning to violence in Ireland.
"The two parties representing the two communities in Northern Ireland have been unable to come together to form a coalition government that they have been able to do over the past 20 years.
"I met both leaders of the two main parties and they both agreed that the uncertainty surrounding Brexit was one of the main reasons why they were unable to form an executive so we can see the uncertainty that Brexit already has an effect if we would have a tough Brexit you can imagine the effects that may follow. "
The previous month told Dr Kate Hayward, a sociology reader at Queens University Belfast, Express.co.uk: "People have forgotten what it used to be like.