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Well, there is a LOT of juice there.
As humans, default game setting, but all events turned off.
Well in hindsight the following is pretty obvious-
The maximum growth for your homeworld is the point where you tax the colony just enough to cover the population growth expense.
Just keep increasing the tax rate until this amount is covered, and the pop growth will keep increasing. As soon as you reach max funding for it, adding more taxes will make growth start to go back down.
The easiest way to accomplish this is to open the colony screen and leave the game running, and just increase the taxation until the growth starts to decrease.
For optimal play, you're going to set the funding to manual as well, set reserve to 0, and adjust the research/pop growth funding to cover them both. If you type a number in one box, and click on the ither one, it will autofill the difference for you.
This will leave you with no cashflow at the beginning, since the planet isn't going to be making enough to cover the expenses yet. You need more population, recreation, medical and luxuries to get to that point.
But after those are taken care of, you will have a small surplus, just whatever is left over from reaching the optimal taxation level.
BUT, the growth rate you can achive is insaaaane. You don't need to have a large positive income at this point in the game, just a couple explorers and construction ships. Income from private ship building gives you plenty for crashing research and paying pirates and indies. Of course you will need to deal with pirates, but that isn't much cost until you've been exploring a few dozens systems and find too many pirates.
But anyway, as Humans, I was getting 8%+ growth on my homeworld, compared to the usual 4.5%ish. Even 10% is possible sometimes if you have a lot of luxuries to boost happiness and income amounts.
In both games, I had more pop than my gizueans neighbors. I also invested into medical on the first one, since i still had plagues on. And i was easily the highest pop even with one other colony.
TLDR takeaway: "The maximum growth for your homeworld is the point where you tax the colony just enough to cover the population growth expense."
There's a lot of other considerations, like research funding and pirates... but when you want to max growth, that's the way to do it.
If possible, raise reputation to get more happiness.
But if you wanted top max growth... Say as an Ikkuro Tall playstyle... That's how to do it.
Another exception would be if your capital is a large and very high quality world with a very large maximum population. Max that out fast.
GIFTS to Pirates and IND Worlds to raise your relations with them, can come out of BONUS INCOME, i.e. the money the Private Economy pays you to build/upgrade Ships for them,
I use Bonus Income to buy things like Colony Ships, which are very expensive to build, and then very expensive to maintain (which DOES come out of Cash Flow).
If you have too many Protection Treaties with Pirates, your Cash Flow can go negative and cut off extra cash spent to double your Research Point production, as well as cut off cash spent to improve the development of your Worlds, including your Home World.
If you can improve Relations (usually by gifts in the short term) with a Pirate Faction enough, you can get a Neutrality Agreement with them, and no longer have to pay that 1500 per year Cost to that Pirate Faction.
Be very careful early in a Pre Warp Game to distinguish between Cash Flow and Bonus Income. If you build too many ships because you have a lot of cash on hand from Bonus Income, the maintenance costs of those ships can really hurt your Cash Flow, i.e. drive it negative.