I assumed you meant precincts, because that's how voting is organized, logistically speaking. Districts are, well, I won't say that they're irrelevant, lest some pedant pounce on me with a cry of "Aha! You don't know what you're talking about!" but they don't really make a difference in this discussion of where and how votes are cast and how someone could interfere with that process. Bringing up counties is absolutely irrelevant, though, and extremely misleading in this context. Delimitation - by which I mean the process of drawing up precincts, or wards, or mini-districts, whatever you want to call them - is determined by population size, not geographic size. For example, if you had a state that had one big urban area with a population of 100,000, and one big rural area with a population of 1,000, you wouldn't drop a polling station into each area and tell everyone to use their respective local station. For one thing, that would make it very easy for any would-be election thieves to rig the whole thing by targeting the urban station, and for another, there's no way that all those urban residents would be able to vote with just one station, even discounting the non-voters among them. Instead, you'd split up the urban area into a number of different precincts with their own stations. It's a lot harder to rig that election, and everyone can vote now.
The same thing applies here. The more densely-populated areas are going to have more precincts, and therefore more polling stations, so that they can handle the higher populations. I'm sure it isn't perfectly even, but each precinct in a state will have roughly similar numbers of voters assigned to them. There certainly aren't any cases where it's so absurdly lopsided that we can just figure that, oh, all they have to do is target this polling station here, this other one over here, and this last one here, and the state is all theirs.