All that you wrote is true and in fact it's stuff I know. The original question is about a subtle detail.

My question comes down to this: how much higher must the charger voltage be for current to flow? Everybody looks at this and says exactly what you just said, but everybody just skips right over what happens between no current flow and some current flow.

Since this is a physics question, we get to imagine perfect parts. I want to know the voltage difference that, with zero theoretical resistance, is required to force the electron to flow. It's not possible that it will flow with no force on it, and force in electricity is represented by voltage.

Now, to what I was asking about: The idea of connecting two batteries, plus to plus and minus to minus, introduces something that doesn't happen with a charger: As the battery with more charge (A) transfers charge to the other battery (B), A goes down in voltage while B increases in voltage.

The question was, will the two batteries come to exact equilibrium, or is there some minimum value of voltage differential that must exist for that last electron to go from A to B? This would leave A with a slightly higher voltage than B. It could be millivolts; it could be nothing. I've not seen a definitive answer to that.

Consider a water metaphor. You've got a dish filled with water. There's a small section of the dish that's lower than the rest of it, and that section is dead level. What happens as we slowly add water to the dish?

The water level comes up to the level of that section, and then rises above it, forming a meniscus, until the force from the resulting head of water is large enough to overcome the surface tension of the water. Water then spills out of the dish. Incidentally, if you stop filling the dish at this point, the water will flow until it's below the height at which it started flowing, but a smaller meniscus will remain.

I'm asking in this battery question if there's something similar going on with the batteries as I've posed the question. Is there some teeny tiny amount of voltage that A must be higher than B for electrons to flow? If not, why not?