"Some like to assert that everybody on Earth could be fit into the State of Texas,..."
My quotations are from this source.
... using logic as follows. The area of Texas is about 262,000 mi2. Dividing this figure by the current human population of 7 billion leaves each person with less than 100 square meters, a small plot the size of a big room about 10 m x 10 m. Sounds plausible enough, right? Without going into the fact that almost half the State is desert, notice we have not allowed for any roads, shopping malls, schools, hospitals, football stadiums, prisons, sewage plants, rivers, lakes, reservoirs, golf courses, parks, and what else? How much land does it take to support a human being?
This beginning statement makes a good point. Removing all other considerations, what's the smallest amount of space a human could stand to live in? I suspect high-density locations like Japan would point out that a 10mx10m room would be more than adequate... but that's all you'd get. Nevertheless, let's continue the story.
Let's do the math again, but this time for the entire planet. The total land surface area of Earth is about 57,308,738 square miles, of which about 24% is mountainous and about 33% is desert. Subtracting this uninhabitable 57% (32,665,981 mi2) from the total land area leaves 24,642,757 square miles or 15.77 billion acres of habitable land.
Divide this figure by the current human population of 7 billion (that's 7,000 million people!) and you get just under one hectare (2.3 acres) per person. If all the habitable land on Earth were equally distributed among all human beings present on Earth, this is the per capita share of good land per person. Again, however, we have not allowed for any nice amenities such as roads, schools, hospitals, shopping malls, rivers, lakes, reservoirs, parks, golf courses, etc. Even so, could you live on 2.3 acres?
Efforts have been made to estimate the amount of land needed to sustain an average individual human (link). A person living the lifestyle of an average American requires almost 24 acres, ten times the world per capita share.
And that's the question, although the article author is being a bit dramatic (and very simplistic). That 24 acres can include space in desert areas (roads, hospitals...) and is shared with others for complex services (roads, hospitals...). While the vast majority of U.S. citizens would fit within this context, there are some (I live near some...) who entirely subsist off the energy grid and entirely provide food and shelter for themselves with less than an acre (it's all about efficiency... and a bit of modern technology). What they can't provide for themselves consistently is water.
EDIT: I need to step in and make couple of a clarifications because some commenters seem to have lost track of the OP's question. The above article is just one of many that have been done to demonstrate — pro or con — just how much of the Earth's surface today's population really needs. One such article I read some time ago used Hong Kong's population density to prove you could crush the world's population into New Jersey. But if you're inclined to argue about the efficiency of the above article, you've forgotten why I posted it. It's nothing more than a means of demonstrating that the OP's proposed circumstance (relocating all of humanity to China, India and Mongolia) is believable. My original answer is about to say this. Arguing that less space could be used is irrelevant.
The second half of this answer is a Frame Challenge that points out that building a world has little meaning if the people reading about, using, or gaming with the world can't understand or relate to it. As alien as the aliens may want to be, leaving your audience confused isn't a good thing. Worse, it's difficult to believe that some commonalities wouldn't exist between humanity and any alien race, not matter how evolutionarily distant from us they may be. The need for food, procreation, education, and science. Competition, whether it be sport, academic, professional, or military. Etc. As was pointed out by one commenter, an alien race that's utterly incomprehensible to us would be unlikely to find any interest in us or our planet — because at the very least, their interest in our planet is something we could understand. Thus, while stashing humanity on a mega-reservation is believable, that an alien race would cross vast tracts of space to do it without a purpose... isn't. And I can't see that purpose, nor was one presented. Anyway... cheers. END EDIT
What's the point I'm making?
What you're trying to do is believable, especially if the aliens are forthcoming with a bit of tech to improve the efficiency, but it's not practical.
- Assuming humanity survived the inevitable "you're standing on my toes!" internal wars, they'd be looking for a way to oust the aliens from day #1.
- Maybe... maybe... we could learn to overcome greed, bigotry, etc. fast enough not to tear ourselves apart (there is precedent, consider Turkey before the Bosnia and Herzegovina independence movement in the 90s), but I suspect the bedlam would be breathtaking.
- If the aliens apply enough outside force to compel humanity into a small area, then your question is kinda irrelevant. You know... aliens with the tech to get to Earth, the tech to move all the humans, the tech to keep them there... can do pretty much anything.
But I would like to point out that your aliens are exhibiting a very odd psychology for conquerors who gobble up most of the planet for themselves.
- Considering the suffering they'd cause among humanity and irritation they'd suffer themselves for as long as humans continued to breathe, such creatures (from a human perspective) would be far more likely to simply exterminate the humans. After all, if you have the power to force this condition upon humanity (8 billion people)... why share?
So, while I find your assertion to be believable from an implementation standpoint, I don't find it believable from a conceptual standpoint. You might think your aliens are trying to show some kind of mercy or something.... In reality, it would be much closer to wanting us to provide gladiatorial sport. Almost anything would be less cruel than to cloister humanity into a small area of their own planet with no hope of overcoming the technological advantage of the conquerors.
And we wouldn't have a hope. Allowing the hope would be a technology dichotomy. A space-faring species that could force us all into a limited area with enough efficiency to realistically stay there and survive would also have the technology to monitor almost every aspect of our society. They'd know if we were getting ahead of ourselves and stamp that out. And we're clever little monkeys... the aliens could be constantly putting out fires, so to speak.
Yeah... I'm having trouble swallowing this idea. Unless humanity was being stored away for slave labor or cannon fodder or some such, I don't understand why aliens would do this. I can't imagine a mix of desperation and compassion that would bring this situation to pass.
But, I'm unlikely to be creative/imaginative enough to justify that as a global assertion.