Is it still the case that provinces stop adding to tech research cost after you have a certain number? or was this removed in IN?

Is it still the case that provinces stop adding to tech research cost after you have a certain number? or was this removed in IN?
The Wiki says that the amount is:
But i don't know how recent that information is.This is a penalty adjusted for the size of your country (in provinces). The piecewise layout above indicates its somewhat unexpected nature; basically, the first two provinces add 20%, and every province after that (except province #6, which counts for double for some reason) is 10% until you reach 8 provinces--at which point you have a 100% penalty (that is, your costs are double that of a one-province nation). Any subsequent provinces will add 2.5% to this modifier per province.
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Why do I have " different " compete merchant chances in every other Cot ? should not they be all the same ?
second, is there a place i can check my merchant compete chances level ?
Compete chance means your chance to actually replace one merchant of another country (compete him out of buisness). If you want to know why your chances vary just hover over the icons of the nation in CoT-window (not the one in the ledger), there you can see what lowers your chance. To actively compete in cot's you either need a high free trade slider or a very specialized mercantile build (all the NI's, high compete advisor, high prestige, no infamy, no non-core cot's)=
Your compete chance is always 50%, plus any bonuses or penalties you get, minus any bonuses or penalties the other guy has. So there isn't one "compete" chance; your compete chance is potentially different against every merchant of every single country out there.
When I enact the "Declare Statute of Monopolies" decision is it still possible to maintain monopolies later on?
If I claim a throne through diplomacy, do I need to declare a war and make the personal union that way or is it possible to gain it simply by waiting for the current ruler to die?
Suppose that I start the game as a Horde (eg: the Timurids) and vassalize some of the neighbouring Hordes. Then I civilize myself... say, by forming the Mughals. Do the vassalized Hordes remain my vassals? Or are they automatically freed from vassalage when I convert from Timurids to Mughals?
The reason I ask, is that a civilized country like the Mughals cannot vassalize a Horde, so if it can be done at all, it needs to be done before civilizing.
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Hmm, didn't see this one in the 'search' function...
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You will get a PU if the ruler dies without an heir with a good claim, but that happens far less then them having a weak succession at some point at all, which enables you to claim their throne.
So, if you really want that PU, War is the best solution. If you want a peaceful PU, you can just claim thrones and hope for the best, but be careful, because you will lose a lot of relations with everyone you have married. Also, if they have an heir with a weak claim instead of no heir, your chances improve vastly, because in this case for you not to get the PU the heir needs to die before the king, and then an other heir with a better claim needs to appear, which obviously is far less likely then just the appearence of the heir before the king dies.
I wanted to add a bit of clarification. It is entirely possible to form a PU with absolutely no negative consequences -- all you need is a royal marriage. However, that's entirely based on luck, and Simberto's dead on with everything else. If the PU is that important, the thing to do is go to war.
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Let's say I have +188% tariffs,
and get a land connection to my colonies (where I have overseas)
Will I lose money then?
"Money" is a tad ambiguous: you're likely to lose "income", but will gain "census taxes".
Whether you will actually lose "income" depends on two factors (among others): a) provincial population and b) tax base. Production income (which represents the largest share of "tariff" income) is determined by units produced, which in turn stem from tax bases and population level. Since overseas provinces' production units are capped to one, population and tax base have little effect on colonies contribution to income. Once you link your colonies to your homeland that cap is gone, thus production income rises.
Generally though, considering average population and tax base in the "New World" (let's say an average, optimistic, 1.3 units in 1600) — 188% tariff efficiency would be more beneficial to you than linking those colonies, income wise.
Portugal, 1492: Tangiers and Ceuta both feature the same high tax base and trade good. Due to distance to the capital one is considered overseas, the other isn't. "Viceroys" was edited so that overall tariff efficiency is 188%.
As you can see, income is higher in overseas Ceuta than in Tangiers.

What do you guys think about trade value?
If I can get +102% trade value. Is that better (and being mercantilism), or is it better to not cut the demand (-50% if not free trade) of my colonies?