What is the maximum extent of the Earth's gravitational dominance?

It is possible for something to escape from low orbit... if it has enough speed.

The Sun's 2.11 light-year "dominance" is the distance to which the Sun's gravity is still higher than the gravitational "noise" representing the combined effect of everything else in the universe.

Beyond that, the Sun's gravity still exists, but is low enough to be considered part of the overall "noise".

IF (a theoretical "if" which does not happen in practice) the Sun were the only major object in the universe, then its "dominance" would extend forever.

The 2.11 light-year is a measure taken in the direction of alpha Centauri (the closest star system). In other directions, it could be higher.

And yet, objects closer than 2.11 can still be "pulled out" by minor interferences from other objects. Tiny planetoids at the outer fringes of the Oort cloud (well inside the 2.11 distance) probably get an occasional boost from some unbalanced part of the "noise" and get to escape despite being closer in than 2.11

Just like some air molecules do escape Earth's atmosphere, just from random boosts they get from collisions with other molecules.

Talk about one of my pet peeves. They should never have thrown away the slide rules.

Are you sure it wasn't 19,961,714,300,000 kilometers? Or 2.10 light years? The precision of this kind of number is perhaps +/- 10 percent, and the rest of the digits after the first comma are pretty meaningless (like 20,000,000,000,000 is close enough).

The effect of gravity from an object diminishes with distance, but it never goes to zero. The Earth is influenced by Jupiter, and Jupiter by Earth, but the amounts are actually quite small compared to the influence from the Sun (and the Moon -- consider tides, for example)

There is nothing like near-zero that is scientific. Is a gravity, 0.001 is near zero, or is it 0.0000001204?

With so many objects even in Earth's vicinity there is nothing like "gravitational dominance" that is determined. There is no such term. It is subjective & only you can say "yes this figure is OK with me".

In Space two or more bodies interact at random so their combined gravitational fields cancel out, get nullified to ' 0 '. It is the possibility that people take into consideration. But with bodies moving these 'points' too move.

In a two body system like Earth-Sun, the Lagrangian points (L1 to L5) are points of zero gravity of either body. I think this is the more tangible, Scientific way to look at the problem.

The L2 Lagrange point of the Earth-Moon system.