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you can send your councillors but unless the surrounding provinces have higher tech, it won't really do anything since there's nothing to spread.
generally if you want to spread tech, you'll want a lot of vassal dukes, since they'll start building the tech in their capitals and that will spread to surrounding provinces.
As long as it is at least a province. If you don't hold the province/county yourself and only have a single holding, then you can't make use of your councillor there.
That#s not true.
Spread happens between demesne provinces and it doesn't matter if they are adjacent or not.
That's two different spreads. Neighbour and demesne.
The Spymaster's "Study Tech" job spreads tech from the target province to your capital.
Councillors' "Research Tech" jobs increase the rate of tech spread TO the target County,
and are cumulative with the Study Tech bonus (but only if the target is your capital).
In other words, what you need to do if you have a less advanced province that you'd want to boost, is to send your Councillors there to "Research Tech", and possibly make it your capital to exploit the Spymaster's bonus.
The ambiguity of tool tips is terrible in game and the wiki is vague on my use case.
I understand how the spreads work and thanks for all the other information, but I have two very specific use cases I would like to understand if what I want to do is possible. I guess I could try it but really have no way of judging it to be effective. So let me write what I want to do and let everyone just analyze it and chime in.
First Use Case:
I have a county on the edge of my realm away from the capital and the tech is terribly low. It is ruled by a count (not me) in a duchy where the duke is my vassal. So its not my demense. The only way its going to get tech points is from the duke and from adjacent spread.
Can I send my councilor to research tech in that county and have the county get boosted or is that a worthless task?
Second Use Case:
I have a merchant republic county about 4 counties over from my capital.
an MR is independent, so not part of my demense.
I'd like to boost the tech there for the better trading practises. Same deal as above, can I send my councilor to research tech there? Will it make any difference?
All you can do is build universities and monasteris in your vassals holdings to increase local spread.
OR...you cheat, play as them and add techpoints via console command, but that's a level of micromanagment that takes the fun out of the game.
in case 1:
As Varainger said build universities and monastic schools (if possible needs at least a certain techlevel), but thats pretty expensive and not really worth the effort.
If the Duke (the counts liege lord) has bad tech too, you could try to get him a county near your high-tech provinces (capital I guess), since the rule that demesne-provinces are neighbouring for tech-transfer counts for him too, his capital could get a slow tech-boost from the new demesne he got near the high-tech area.
This is also somewhat problematic since you need the county to give him (probably upsetting some of the order in your realm) and he could give it away to a count-vassal of his own, so it wont be in his demesne any more and the direct transfer to his capital would be screwed.
in case 2:
Best is to send your steward to your own province nearest to the MRs capital (unless it already has the highest trade-practice tech you have), to boost trade-practice tech there up as much as possible.
Tech-transfer is faster the bigger the difference between provinces is. So lets say province A has level 2 and province B has level 1, tech will bleed over very slowly. But if A has level 4 and B has level 1, tech will bleed over a lot faster (until they get closer to each other ofc, then it slows down)
Especially in case 1, if you want to boost tech in a distant part of your realm (for example if you start in england conquer all of Britain and want to boost up scotland and ireland) it can be a good idea to keep a single demesne-province in the heart of the low-tech area and boost that with councillors (if they don't have more important jobs to do).
A) Tech will already slowly bleed over from that province to your vassals in the area
B) when you manage to push that province up give it to a vassal duke or king in the area
Tech-transfer always works faster under the same ruler:
Demesne of the same ruler -> fastest
Same Realm -> normal
Different Realms -> slow
Also if you want to tech up a realm getting the city-builder blood-line is a good idea, since it allows for EVERY ruler in your realm (so no matter if they are your direct vassals, vassals of vassale or even further down the chain) to build a new building in cities, that generates more income and gives an additional tech-transfer bonus.
So owning a county in the heart of tech poor zone is key. Ok got that.
But putting my steward there will increase tech? I thought thats not how that works, or since its my county, then it works? What about crown focus. Do that too?
University though are ridiculously expensive (they generally cost around 8-10x (or more) as much as a temple school), so you'll generally only want those in provinces that are REALLY important, but you can also just leave it up your vassals to build them.
Eventually they'll run out of other stuff to spend money on and build the universities.
The Steward increases the tech-spread, tech-spread is basically your chance to pull in 10% towards the next level of a tech from neighbouring provinces.
Since demesne provinces all count as neighbouring for tech-spread no matter where they are geographically it will help.
Crown focus afaik does nothing to increase tech-spread, it can trigger positive events and if you have reapers due (DLC) the province prosperity will usually rise a bit faster.
(at prosperity 3 and crown focus active the province has the chance for an event to buy an additional holding slot)