With a Gargoyle, unravelling at the Queen's Soul Forge, the total intensity of the item has to be at least 401%, to give relic fragment(s). With a human or elf, the item intensity has to be more (451%+, I think). The total intensity needed for Enchanted Essence is 200%+, less than that will give a Magical Residue (I don't know the specifics for gargoyle and human/elf intensities, as items of this quality are easy to find).
If you are unravelling Imbued items, there is something inplace to consider them lower quality than they show (the total intensity is fractioned, for the purposes of unravelling). This was done to prevent Relic Fragment crafting, from Imbuing alone.
There is a stickied thread in the Craftsman Data Chest on what artifacts yeld when unravelled:
[Imbuing] Artifacts Unravel to the Following Ingredient
Stayin Alive,
BG