Its easy to get enough credits in most medium maps or larger. The limit is crystal or metal. By centralizing your HQ you can maximize resource outputs. This is especially true in multi-star empires where the phase jumps can really add up. Now, when does it pay off? I think you'd have to calculate like this: Sum (#mines (each mine weighed against allegiance)) in original layout vs (#mines (each mine weighed against allegiance)) in alternate layout. Then delta(output difference) x (X) = cost of changing HQ, where X is solved for how long to 'pay' for the upgrade.

Eyeballing it, the improvement often seems 'worth' it to me ~ 20 planets, especially across multiple stars.

If you had 5 planets in an X shape , moving the HQ from a limb to the center would raise your total max allegiance from 480 to 510, which isn't much.

9 planets in an X shape, moving the HQ from the edge of a limb to the center would raise it from 750 to 870. (16% bonus on average to each resource collection)

Obviously an X would be rare, but this gives an idea of the kind of gains it can bring.

There's a few factors to determine if it's a good idea: The the size of the galaxy, the vulnerability of said planet (If your hq gets sacked without another one being built, it will do a lot of income damage), and the intended length of the game. If you plan to attack aggressively and have the battle end in 30 minutes, it may not be a good idea, but if you're playing at a leisurely pace, and maybe aim for a several hour game, then you should definitely move your hq around.

The capital gives a tax bonus, but I forget if it's percentage based or just straight added in.

I believe the capital gets a tax bonus based on the type of planet it is (or possibly based on its population cap) . . . I've seen Terran worlds get a 4.0 credit boost for being the capital, whereas asteroids and volcanic worlds get something like a 1.0 or 2.0 credit boost.

(Also, I don't think it's linked directly to population, because I've seen someone bomb my Terran capital down to 0 population and have it still be producing 4 credits/s.)

I don't think you actually *can* make an asteroid your Capital. Or am I thinking of a dead asteroid?

This obviously depends on the situation.
The main reason to move the capital should be for the increase in mineral income. Credit is not as much as a concern because you can always build trade posts that give lucrative income without limit. Refineries, in contrast, are not as effective.

But there is a map that i always move my capital. In Entanglement where you always start at the end of an arm of the solar system, players are forced to expand quite linerly,so alligence drop by almost 50% after a few planets.No choice but to make a move