The Irish land border

I have been curious about the debate over the post-Brexit land border between the UK and Ireland. If Ireland is in the EU and the UK is controlling immigration from the EU and is outside the single market then I do not see how one can avoid having border controls. I am reminded of the Scottish independence campaign where the SNP included among their implausible claims that they could define a separate immigration policy for Scotland yet retain an open border with England.

I guess I can see that Northern Ireland could allow less reliable immigration control than mainland Britain; there could be another series of checks for entering the rest of the UK^*. Perhaps there could even be some special way to distinguish goods for customs so that containers can transit from Ireland through the UK to mainland Europe without having left the EU in any strong sense.

Still, for any meaningful Brexit how travel and commerce between Ireland and the UK could avoid being impeded I find it hard to imagine, however anxious Ireland might be for routine intercourse to remain unchanged. I wonder what realistic solution the EU would accept.

^*Update: I failed to appreciate how strongly the Democratic Unionist Party would object to such.