What will be Asia's energy consumption in 2100?
The US currently uses 300 GJ per capita per annum. China is at 76 and India is at 24 GJ per capita, currently. Lets say that with rising wealth but improved electric efficiency, Asia uses 100 GJ per capita.
According to the UN via the Washington Post, Asia is set for about 4.5 billion people in 2100. Multiplying those numbers, we need 4.5e20 J of electicity for Asia in 2100, or 14 TW. 75% of that is about 11 TW of electrical power.
Can a fusion generator generate 11 TW?
For massive scale fusion power, the tokamak is probably the only way to go. There are a great variety of potential reactor designs, but the tokamak scales the best...by far. The premise is that you create a toroidal magnetic containment field and then heat fusion fuel inside of it to 10 keV or more. Fusion ensues, and once the temperature gets hot enough, the heat production exceeds the input requirements. You then extract the heat in some manner and generate electricity. A significant portion of this electricity would be needed to generate the magnetic confinement fields. Whatever is left over can power the grid.
Because of the magnetic confinement power requirements, a tokamak works best at the largest scale. If one is ever made, I would expect it to be on the 100 GW scale or maybe even more. It is not inconceivable that you could make TW tokamaks, and set up a group of them in one spot to generate the necessary power.
Can Tokamaks be built by 2100?
This is the question that you as the author will have to answer. There are three primary problems with tokamaks thus far.
First, D-D or D-T fusion produces very high energy neutrons. These neutrons will rapidly activate and embrittle the materials of the tokamak. There is no practical way to stop the neutrons, so either you will have to use a low neutron reaction (called aneutronic; some combination of H-1, He-3, Li-6; or H-1 and B-11). The other option is to develop materials that can sufficiently withstand the embrittlement for the decades of the life of the plant.
Second, the scale of the necessary magnetic fields is very large. In order to generate more energy than is required to operate the field, we would need better magnets than we are currently using. The big technological advance that would solve this problem would be better superconductors. With some advanced superconducting electromagnets, it would become much easier to generate the necessary magnetic fields to contain the very hot plasma.
Third, the understanding of magnetoplasmadynamics is currently insufficient. There are instabilities brought on by the fact that a plasma will have an induced current when exposed to a magnetic field. There is potential for Mega-Amp currents to develop inside the plasma, which will then create its own magnetic field and potentially result in a loss of containment. Solving this problem requires a lot of primary research in to plasma physics.
So can we have a tokamak by 2100? I'm optimistic that the answer is yes. The problems are significant, but reasonably well understood. Dedicated, persistent funding should be able to unlock the necessary physics in a few decades. A little engineering determination later, we could have a working reactor with positive net energy.
How would Asia share the responsibility?
The first thing to note here, is why would you ever make a single reactor? Lets say we have average consumption of 11 TW, and peak of 15 TW. It would be best to have 5 installations of 4 1 TW reactors each, each in different locations. Single reactors are single points of failure. With so many reactors spread out, each facility could take one reactor down for maintenance and still meet the peak power requirements. You mention the seabed...I'm going to ignore that, that is not a good idea.
Since splitting the reactors is basically the only way to do it, they would likely be split between countries who would then sell power to each other. Russia, China, and India are obvious destinations for a powerplant; Iran and Indonesia would probably be next. You can pretty much divvy up the plants between countries any way you wish. If you insist on a single plant, I will tell you that a single plant powering Asia is extremely unrealistic.