Dominion is pretty complicated, though the manual has a decent explanation. (by the way, I don't think anyone has yet pointed out to you that the game comes with a 292 page manual. It does not include stats for the basic national troops, but it does include full stats for every kind of maigically summoned troop - which is far more important).
The short answer is that all troops gain morale in + dominion and lose morale in enemy dominion. Your pretender and prophet gain/lose hitpoints based on dominion. A few pretenders and troops are immortal - but only if they are killed in friendly dominion.
Dominion is spread to surrounding provinces by temples, your prophet, and your pretender. Preaching can raise dominion, but only in that province.
There is an indirect chance to 'flip' - high enemy dominion increases unrest, high unrest can possibly lead to a revolt, which would flip the province to independent - but don't expect to ever see it happen in a game.
A province of yours under enemy dominion will suffer from any negative scale effects, but will not benefit from any positive scale effects.
Like I said - that's the short answer
Re: Problems in demo exist in regular game?
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