Theresa Villiers - the current Northern Ireland Secretary - a leave supporter - assures us that the border would remain as open as it is now, in the event of a UK withdrawal.
If she really knows....
http://www.belfasttelegraph.co.uk/news/eu-referendum/villiers-leave-vote-wont-see-return-of-irish-border-checks-34628950.html
Not everybody agrees with her, though.
http://www.bbc.co.uk/news/uk-northern-ireland-36448599