Limit of dynamic memory on video cards

I tried to gather some infos out there but I think I need to summon the league of the vvvvise men … is there any limit to the amount of memory a video card can access on the main system, any difference between integrated controllers/APUs and PCIe cards? And whatnot? What happen when the RAM is accessed from the vidoe card, will only that portion be slower or will it slow down the whole?