[thejeff]

Look in the manual for the exact formulas.

Briefly, each temple (and the prophet and god) causes a temple check, based on your original dominion. If this is successful a point of dominion is generated, this can then either raise the local dominion or propagate outward until it either raises dominion in some province or fails to lower enemy dominion somewhere. There is a check based on the current dominion in each province.

Preaching only raises dominion in the province being preached in. This is useful for provinces under enemy dominion or to boost dominion so temple checks are more likely to propagate into enemy dominion. Preaching only works up to a max of Holy level or Holy*2 if there is a temple, and you'll get a message to that effect when you start preaching in a province with higher dominion. That message would make no sense if preaching spread dominion to other provinces.

Blood sacrifice generates one temple check per slave. It can be brutally effective since, with a Jade Knife, you can get 4-5 checks from each province, allowing dominion spread to be focused against an enemy.