Titanite Breakdown

Remy the Rat can bite and break titanite into smaller pieces. This can be done at any time of the game and the only requirement is having the item to break in the inventory.

Initial Item	Resulting Item
1 Titanite Slab	5 Titanite Chunk
1 Titanite Chunk	5 Large Titanite Shard
1 Large Titanite Shard	5 Titanite Shard

Information here is accurate for version 2.15.