It will presumably mean the Irish Republic staying out of the Schengen zone (as at present). I can't forsee a situation where the UK would want to restrict EU nationals visiting, therefore it would make little difference if they decided to enter via the scenic route.
Perhaps there will be some way of the UK and Irish Rep border authorities sharing information on particular individuals whom we don't want to let in. The Irish Rep might not stop them, however there might be an agreement to tip off the UK authorities that so and so has arrived in the common travel area so that the police can keep an eye out for them.
That would mean, I assume, someone who had come to the UK via the mainland (Dover/Heathrow/whatever) and not being allowed a work permit due to Brexit's points-system (whatever that is), being refused entry and then they try the Irish route?
Obviously they cannot by EU law be prevented from entering the Republic, so would the Irish have a legal right to inform the UK that someone who has not broken any EU law (it won't be a criminal offence to leave the EU in search of work??) MAY attempt to cross an open border?
And even if so - should both countries authorities be spending vast amounts of money on resources to track someone who merely wants a job?
If it were a known terrorist on the other hand, they can and should be prevented from entering the UK as it stands now. No need for Brexit.
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The solution is of course the Swiss model. EU/EEA nationals are freely admitted (except where they are wanted or pose a threat to security as can already be done), but they require a work visa of which there are a set number each year. Might not be politically acceptable or may lead to increase in illegal employment, but it's realistic. That way the Border Force maintains its ability to function without grinding to a halt.
That's the obvious solution (therefore we might as well be part of the EEA). However will Brexit accept that there is still total free movement of EU/EEA citzens, but instead of them all obtaining legit work, some will and the others search for illegit work?