no offense bulk_4me, but he was right when he said that he want answers from people who understand his questions, he asked a way to get AA and AF to work with Radeon cards, not a way to make the gridlines disappear by turning AA and AF off, you could simply keep it on quality and remove AA and AF of you wanted that, also i have a ATI card on my other PC, i never found a way to get the gridlines to completely disappear, but i suggest you try changing some things in the registry:
HKEY_LOCAL_MACHINE - SOFTWARE - Square Soft, inc - Final Fantasy VII - 1.00 - Graphics // Mode (mine is currently set to 2), but try changing that to other numbers, and to the others, yes this only changes the mode which is set to Riva or TNT. but somehow mine worked when i changed it manually.
Also to run registry, Run - Regedit
good luck trying that out.