Contradicting the pessimists, a bit

Piz:

What sort of terratory would it be? Tiny obviously, because of the number of people willing to be involved in establsihing it and running it.

Not necessarily.

The big people of the Eastern Slavs invited a few Swedish warriors to rule them. Today, that's Russia.

A few hundred crazy Europeans of several nationalities decided that the strange lands to the West were cool. Today, that's the USA and Canada.

A few hundred crazy farmers decided it would be good to expand their farms into the practically void wilderness to their south. Today, that's Argentina.

And almost certainly dirt poor and baren because while the idea of a country giving up some of its terratory is implausible at the best of times, it gets downright laugable if we imagine the terratory in question to have any worth in terms of natural resources, agriculture, etc.

1) Depends partly on how you got the land. If you simply replaced the ruling class from the top down, you can, at least in theory, take any territory you want. A simple way to do this might be coordinated migration (like the Germans invading Western Europe during the Fall of the Western Empire) - but the current trends of migration laws basically everywhere seem designed to prevent exactly that.

2) Don't tie your economy to the economic models of ancient times. Hydroponics can perfectly replace natural soil agriculture if done well. No other resource is so vital, scarce, expensive or impossible to substitute that it would be impossible to acquire in the market. Remember too, that for every product there is a black market. A trade embargo tells you who your friends are; but doesn't make it impossible to actually trade when there is someone willing to sell.

So Utopia looks like a pretty small, bleak place with not much prospect of getting an economy going within its own borders and little chance of trade with the outside world due to international outrage at the existence of a paedonation. Not that it would have much to trade anyway.

If I were the Paedo-President, I wouldn't hesitate to legalise and openly trade illegal products like opium, cocaine, kp, blood diamonds, and money laundering. At least, not if the rest of the world ostracises us. But if you are ostracised, then you could at least find enough powerful allies inside basically every nation in the world - those who are buying your products.

There would be no kids. Adults there of their own free will could renounce the citizenship of their native countries. I don't see many counties recognising the right of minor citizens to do any such thing. As such, minors ending up in such a country would be treated like that country's children being taken to a rogue paedostate to be sexually abused. That would be as good a reason as any to invade such a terratory and wipe it off the map.

That too depends on how you got the land. The ruling class displacement model doesn't prevent kids from being there. Even in the New Land model, it's not a given. Many MAAs are not exclusive, and / or are parents. There is nowhere that I know a rule that only MAAs can migrate to such a place; and it wouldn't have to be such an unattractive place as you believe for other prosecuted minorities - racial, ethnic, religious, political, tax evaders... Nothing prevents us, either, from raiding the orphanages of other countries. Or simpler than that, provide a "drop your unplanned kid at our embassy" everywhere.

To be honest even if they were allowed in by their parent countries or were born there, Utopia with no economy, no modern heatlhcare, no universities and no friends internationally sounds like an absolutely hideous place to grow up, even if you get to have sex with all the adults. I would not try to elope to a place like that with my LGF.

I expect to have answered the part about economy.

The healthcare should be solvable if enough people are physicians, to being with, and at least some are top level physicians - capable of running a good hospital and capable of placing orders for the correct technology to countries that produce it - and eventually, probably capable of having it made domestically.

Universities are not strictly necessary. They are there to give horny 18yos some place to get laid, frankly. And so that the degree can be standardised to such a point that everyone can be categorised as "having" or "not having" and as "good degree", "bad degree"... But if you want higher learning, there is nothing that prevents you from acquiring it outside universities - all the knowledge that is transmitted in a university class is already on books or on academic papers. Yes, some subjects do require labs or special facilities to be learned properly - but nothing, either, prevents us from building some of that. If you mean to build a CERN, then yes, we'd be off the mark. But that's not the only possible lab we can have or need.

As for international friends, no country is absolutely deprived of them. Of course, there are degrees to what others will defend you. But Goethe is right that anti-Western countries, which could include a reasonable number of old Eastern rivals and emerging powers, might have incentives to at least speak to you - which is always useful. There is always the risk to become an Iraq or an Afghanistan that nobody defends - but it will depend on many considerations, and, again, if you can get covert domestic allies in officially unfriendly countries: obviously the West isn't invading Burma and North Korea because they are too close to China; but the same West isn't forcing the Israelis out of Palestinian lands because of the Zionist lobby, and as hard as the USA speaks of Cuba, they won't invade it because the American Cubans, knowing their families would be at greater risk from the US army than they are from the socialist regime, prevent it. So, get domestic allies. They're useful. And be in talking terms with as many people as possible - even if they are all rogue states. And don't make nukes. There are better weapons anyways... / or make them too fast, before the rest of the world can react, so that when they do react, they are anyway already deterred from attacking you...

Dante:

These days you need an army to defend your borders and enough powerful allies that the world won't stand idly by while armies come in to dismantle what you've built.

But wars are no longer won by "who has the largest army"...

And being an ally doesn't necessarily mean "being an ally". I don't think the West had any interest in Kosovo whatsoever - they had an interest in containing Miloević's Serbia, which is different. Sometimes, choosing your enemies is more important than choosing your allies...

Goethe:

I admit that I've always believed more in...
a) the ruling class replacement model (by which we would take an existing country by taking it top-down)
b) the coordinated migration model (by which we would take an existing country by taking it bottom-up)
c) the New World model (by which we take basically by force a relatively empty, ill-defended, piece of land, not necessarily unclaimed, but ill-defended)
d) the de facto state model (by which we have *both* coordinated migration into, and partial ruling class replacement, into an already existing de facto but unrecognised state. Do I propose Transdniestria, and you Somaliland??)

But the buy-out model has virtues too - it'd be faster than the four above, and would be less violent than (C) is and (D) can get.

I see many places where it could take place, actually, and in all continents except Western Europe; all of that depending on other conditions, of course.

The incentive for a country to do that would be the settlement of an area that was previously unpopulated or sparsely populated; and probably also the management or development of that area's resources without cost to the central government. I don't see as impossible to be granted outright sovereignty - but I do see it as difficult. And I see as unavoidable to be conditioned to enter into pacts and alliances with the donor country. I also don't see autonomy short of sovereignty as unworkable - there are thousands of precedents of such agreements between central governments and religious or ethnic minorities. Of course, not every country would agree to that, either, and these types of autonomies tend to diminish, not grow, over time, so I'd see it as an inferior option to sovereignty.