In the EU, having a shag does often equal residency rights when the shagged party wants it and is willing to move to another EU member state where their mobility rights are operational and the shagging is continuing for who knows how long. [Many one-time "vacation" or internet "romances" have been part of the picture of approval of residency, at least on a temporary basis. (Most of the problems arising from such are related to the policy of the residency right being temporary and conditional, keeping the "foreigner" in a difficult dilemma when already under duress caused by the EU citizen with whom they are related in the eyes of government.) Trafficking of people out of the EU is a less frequent problem even as it plays to the tabloid-reading audience quite well.]
A shag singular, rather than ongoing shaggums! An ongoing relationship, living together, etc. is something quite different to a one night stand!
The family rights in the EU, to also be availed by non-EU persons depending upon relationships with some EU citizen(s), are already often exercisable in the EU when an EU party is able to settle in another EU member country and make a go of it first.
Would that be under the normal immigration channels?
On a separate note, I was under the impression -- perhaps mistaken -- that countries are actually expanding the numbers of children granted citizenship of the birth country despite being children of non-nationals at the time they were born in the country. I certainly have run into an increasing number of such people in recent years than I would have a decade or two or three ago.
I don't know about all the countries, but I know the UK (1983) and Ireland (more recently) stopped the automatic citizenship - now, if you are born in the UK, either a parent has to be a British Citizen themselves, or they have to be legally settled - i.e. a non Brit in the UK illegally giving birth would not normally get citizenship (there are some really funky rules relation to stateless persons, but that is normally things like when the parent was a citizen of a country that now no longer exists, and thus are stateless themselves but those are very much the exception). Caused some real headaches in a slightly more complex way for some where parents and grandparents and the child were all born overseas / in British territories - got very bogged down with some of that paperwork!
I will (if allowed) happily get around to responding in full to the above post (by editing this post at some point in the next two or three days). [I have to exercise some more passport-free international travel rights, even as I have a few passports that I ordinarily use for most of my travels.

But first I need to book a bunch of my own trips.

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