Can you find the post, it would be interesting read.

 

These bonusses are additive. Meaning that if you have a world with 50 production and +150% manufacturing from buildings and a world with 50 production and +0% from buildings you get the same amount of manufacturing out of the capital (ignoring adjacencies). Same goes for ghost worlds and tech capitals. A ghost worlds gets more out of a thullium data archive though.

The reason I put these on my homeworld is that I want these bonusses early in order to make most use of them (if I don't rush them the capital is the only world that can build them in a reasonable time frame). Plus early my homeworld has the highest pop and the civilization capital has a few better bonusses then the colony capitals. I believe I get more out of developing my homeworld early like this. My homeworlds are often comparable to the terran one, because I prefer the early growth rate of a second world over having a class 16 starting world.

You said you wanted your mnufacturing capital on a world with lots of space. So let us assume you have some additional mnufacturing buildings on it:

World A has 50 Production and no manufacturing bonusses, slider is 0.2/0.4/0.4 W/M/R:

Manufacturing = 0.4*50*(1+0) = 20 manufacturing
now you add manufacturing capital (ignoring the additional adjacencies (~5-20%)) you get)
Manufacturing = 0.4*50*(1+200%) = 60 manufacturing
-> your manufacturing capital gives you 40 manufacturing

World B allready has 4 basic factories (110% manufacturing with adjacencies) and pseudo ghost world (+50% manufacturing to planet, I know there is no such thing but I will use it here to explain why ghost world has no impact on whether or not you want to place your capital there), 50 production and same sliders as above

Manufacturing = 0.4*50*(1+110%+50%) = 52 manufacturing
now you add manufacturing capital (ignoring adjacencies again (~40-50%)) you get:
Manufacturing = 0.4*50*(1+110%+50%+200%) = 92 manufacturing                          (*)
-> your manufacturing capital gives you 40 manufacturing

(*) = Here you see what I mean with the bonusses being additive: It is 1+110%+50%+200% = 460% and not (1+110%)*(1+50%)*(1+200%) = 945%; then it would be considerably better to build your capital on a big world.

So I ignored adjacencies so far, but they make no difference if you make a specialized world and are able to surround your capital anyways eventually (possible on class 12, especially on Earth you can reserve a spot like this).

So what will happen that makes the capital on a large world better then on a small world is the terminal population size of the planet (whenever it is reached), because this contributes to production and therefore multiplicatively towards your total W/M/R.

But all this said, my second paragraph was the more important argument for putting them on my homeworld.