My car had ~2 awg from the alt to the batt. I am upgrading to 1/0 because I'm getting a HO alt anyway, so why not?
The only way to solve dimming completely is with both batteries and a HO alt. With just an alt, voltage will be all over the place due to the demands of the amps and not a lot of reserve to draw it from. Batteries add a ton of reserve, but they do need something to charge them. Unless you play a ton of tones or rap with long bass lines, batteries normally solve everyone's problems. Music is dynamic. But if you listen to everything, like me, you probably need both.
I'm debating right now on what I should do for batt's. Thinking about an HC800 in back, then upgrading the front to a hc1400. Then I'll hopefully be set.