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Question

Heres a hypothetical question: If you have an unlimited supply of hydrogen. Unlimited heat and gravitational pressure, could you keep fusing atoms together indefinitely even past fusing elements such as uranium together. What is the limit to how high you could go?

Answer 1

Stars pretty much do this - though they don't have unlimited hydrogen or gravity.

When a star fuses hydrogen together, it makes helium (and energy, which keeps the star glowing, and keeps it a stable diameter, balancing the inward force of gravity).

When the star runs out of hydrogen (statistically, there aren't enough H atoms next to each other in the core to fuse together), it moves on to fusing hydrogen and helium (making Lithium) or two He together (making Beryllium). This might produce more energy (so the star grows) or less (star shrinks), and is called "going Nova".

All the elements heavier than Hydrogen are made in this way - in the heart of a star. And over its lifespan, the star will go nova many times.

Eventually, however, the star reaches Iron. When you fuse two Fe atoms together, it takes more energy than it produces. So the star is no longer self-sustaining, and the core collapses - incidentally producing all elements heavier then iron (like gold, the gold in any jewelry you wear was made in the heart of a dying star). when the core collapses, the star explodes, scattering the elements across space.

Without infinte gravity and fuel, this is as high as you can go.

If you truly *did* have infinite gravity, then it would be more than enough to overcome any repulsive forces in the atoms you were fusing, so eventually all the matter would be compressed into a vast black hole.

Answer 2

Not very far at all, if you only have standard hydrogen, which has no neutrons.  If you make neutrons, then you should be able to fill the periodic table.