economy starbases confuse me

Apples and oranges.

The line from a Mined asteroid square to a planet is the flow of production resources to that planet. That is, the asteroid resources are being beamed through subspace to the planet; no ships involved. The effect is to add to the "hammers" for production available for that planet.

Economy starbases are essentially collecting tolls from freightliners that pass through their Zone of Control. (Left-click on the starbase and a ring will appear on the map surrounding the starbase.) Once a freighter makes a route by traversing from point of origin to destination, you are informed about how much per turn that route is worth. There will be an actual ship that makes the route, appearing at the origin and going to the destination at a speed of 1 square per turn. (Sllloooowwww.) If the route passes through a econ starbase's ZOC, you get a percentage of that revenue. I can't recall if you get a percentage every turn, or if you get money only during those turns that the freighter is actually in the starbase's ZOC. (I think it's the former.)

I haven't built any mining starbases yet, so my advise will be limited to economy in general. One point though, did you research the necessary tech to be able to build mining starbases?

As for economy:
1) Morale only needs to be high enough to have a good population growth early on. In the late game, you can have morale just above the point where you'd lose population on your least happy planet (mid 20% if I remember well), except just before the election, then 60-70% is a safe choice. Just increase taxes according to the minimum morale needed in the late game.
2) Research economy & morale techs, more advanced government types.
3) On your homeworld, at least 1 morale building will be necessary - or a political capital. Otherwise you'll need extremely low taxes to keep your population happy. On any planets with farms, additional morale buildings will be needed.
4) Consider changing some lower quality planets to economy only. Specializing them in research or production won't make such a vast difference if you already have higher quality planets doing that.
5) Improve any starbases you have on resources (the crystal-like resources, not the mining ones) to their maximum, except for influence unless that has some use for you. But improved research, morale, economy all help to maintain a better economy.
6) Trade routes don't do much anymore in TA but having up to 10 trade routes helps a little.
7) Economic alliances, especially with AI's who have an average or strong economy.
8) Selling non-diplomacy techs to AI's, even weak military techs. This doesn't solve the economic problem but at least gives a cash boost.

Also, check where your biggest expenses are, why are you still struggling with the economy in the late game? Can you improve things by changing the slider settings?
Check your spending on espionage, any chances of reducing that a little?

Economy starbases have nothing to do with asteroid mining. They add value to trade routes that pass through them. Frieghters and miners are different (to answer your question). There are 3 mudules that add to trade route value and i believe they are unlocked by reseraching each of the trade techs.

I don't usually build economy starbases for trade routes though. They will add upto 24% (thats DA & DL, I'm not sue which races can have all of those in TA)to the production of any planet within their influence radius. That is to military, social and reserach. Have a few of these around your tech capital for a naice boost in research. I play with tight clusters usually so that i can have a lot of planets for each starbase.

ok this is all sound advice. yet.... my original question was not answered in the slightest .

as for going in red late game. perhaps we are not agreeing what "late game is"
I usually try to end A game As quickly as possible. so I may build A large army of transports and position them to make one big sweep and take over like 25 planets on the same few turns.

sure this ruins me economywise . thats probably due to me not going about it peicemeal and letting a group of conquered planets stabilize first, before moving on to the next group.

all of this is purely playstyle and is off topic of what I need to know.

what i need to know. is why the AI is putting ECONOMY starbases on its asteroid mining paths .

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Sorry, but i don't know why the AI would do that. Could be that it has nothing to do with the mining but becuase it has / had trade routes through there.

What the AI does with star bases can be baffling at times. I've seen minor races fill an area with influence bases. I've also had the Torians build about 6 influence bases with no additional modules in the vast empty space between me and the Acreans. There was no way they could have benefited from them. So maybe they just had some extra constuctors.

Maybe a frighter route was going across the mining starbase rails?

Coincidence. The freighter routes probably pass along the same path.

Somehwere in Options are a couple choices that will show on the map A) Trade routes, and resource paths from asteroids to planet of destination. Toggle those off and on and look at the map. Just to clarify things even more, Assign the Mines to a planet far away in order to move the resource path away from the planet in question. (That is, if the Mine is yours to control. If it isn't, then the path simply is what it is. At least you'll be able to see it.)