I apologize if this has already been mentioned, but the Remnant's that drop from Notorious Monsters in the Mea, Dem, and Holla areas are used to spawn other Norotious Monsters in Promvyion - Vahzl that, again, drop Remnants which can be traded in to get equipment from the Empty Memories quest.
The entire process can be found on ffxi.cannotlinkto, although it does not detail which remnant from the Vahzl NMs grant which piece of equipment.
The rewards, briefly, are as follows:
Hamayumi
Lv 30, Rare/Ex
BST DRK NIN PLD RDM RNG SAM THF WAR
Additional Effect vs Empty: Ranged Accuracy +10
Additional Effect vs Empty: Ranged Attack +10%
Dia Wand
Lv 40, Rare/Ex
WHM
Enhances "Cure" effect
Enhances "Dia" effect
Stone Gorget
Lv 39, Rare/Ex
All Jobs
Enhances "Stoneskin" effect
Edit: Opps. I apolgoize for the bump, I was just browsing through the Interactive Promathia guide, wound up here, and noticed something that the OP had a question about. :3
Edited, Mon Aug 22 15:56:56 2005 by Iresire