I have searched the game files and the definition of dominant culture seems to be hardcoded.
So basically nobody knows what determines a dominant culture but this seems to be consensus:
A culture will become dominant if the total base tax of the provinces of that culture which you also have a core on is big enough compared to the total base tax of all other provinces you have a core on. Some believe it need to be 30%, others believe it need to be the largest - which can range from 51% if you have only two cultures or any other percentage as long as it is the largest.
I found it to be more difficult than that in (the first version of) my current game. Non core owned provinces play a role in it too, provided you play IN 3.2beta.
I am playing a Mecklemburg turned into the Netherlands.
On my first effort I took all and only the dutch provinces, then I got a bunch of other ones with the plan that I would switch to dutch culture AFTER the dutch provinces cored but BEFORE the other ones would. It simply did not work. I do not know the exact rule, but I suspect it has something to do with the "cultural make-up" of your nation as shown in the national statistics pie chart.
On my current run I am doing something original and clever, I hope.
I
started as Mecklemburg and I conquered the dutch provinces, switched culture,
formed the Netherlands. The reasons are two and both lead to trade power:
1) you start with a core on Lubeck and you get a core on Antwerpen, how does it feel to own the two biggest CoTs of Europe?
2) you can
join the Hansa (hard coded into a fistful of blessed nations, Meck is in but no dutch is allowed) AND
get the Netherlands 2 unique decisions which are mighty good for traders.
I then sold the dutch provinces to a handy vassal while keeping the flemish ones conquered in the mean time. Building workshops on all and only the pommeranian cultures (I conquered the missing two provinces a while back) I was able to
switch back primary culture to Pommeranian!
Why? But because I can now
form Prussia and Germany, of course! Yes, Prussia: normally people go through the "Saxon way", but the pommeranian way fits my strategy better. I want to build Germany by blocks: first a (superior) northern trade powerhouse created by the fusion of the old Hansa and the new dutch financial and colonial ventures, which wields the (superior) imperial title. Then a (superior) protestant force which turns into a military Great Power (or more fittingly, a Superior Power) and vanquishes the Hapsburgs, the Pope and France. Then the unification of all the (superior) lands of the old HRE into a (superior) German costitutional republic (you are protestant, have a nice bunch of global_trade_modifier boni, a rich land AND an event giving you cores and +1 base tax almost everywhere).
Sadly my plans got a bit scrambled in around 1450, when I got to lead a
personal union with... France. Now it is 1490, I am Johan the first, king of the Netherlands (got the strategy), Holy Roman Emperor (got the german vassals), Papal controller (got the trade money) and King of France (got the luck).
I have oozes of manpower but I DON'T NEED IT, because something blue fights my wars for me, and everything it vanquishes is formally occupied by me. Today I am ALWAYS fighting a war, because otherwise France would insult me. I have been crusading against the Ottomans in order to be able to get some action for myself.
Still France managed to siege Achea. France got the "rule the seas" mission, so it built a killer fleet as big as Englands and can be found everywhere, now. I was shocked when I saw ALL France's coastal provinces building ships at the same time, and I checked what was going on.
Why the Ottomans? Well because of the crusading bonus (as the Papal controller, I called the thing) and mostly because I am a free trader and I want the Black Sea Trade event. So I conquered Bursa and Costantinople after the Ottos squashed Byz but before they moved the capital and I BUILT A COT in it. I am about to sell the province (with a CoT!) back hoping they move their capital in, so that I can finally conquer Edirne... it's fun
My money is spent in influencing Cardinals to clean my hands of the blood I must spill to keep France busy, and in gifts to France to keep relations up so that, some fateful day, I will inherit...
It would be sweeter if it happened after I formed Germany, but I wonder what will happen when I convert to Protestant!
I am wondering if I should make it into an AAR. Anyone interested?