A Tier 0 cannot have parts
This naturally follows from the requirement of it being completely devoid of differentiation. All-in-all, the character must necessarily be completely indivisible and irreducible to anything more basic than itself, and therefore smaller "parts," "pieces" or "fragments" are things that it cannot have.
Consequently, there can be no such thing as partitions of that being's power, either. No such thing as "He was only using a small portion of his energy!" and the like. And neither there can be such a thing as "A small part of its totality," save as a figure of speech.
Mind you, this is not in a "Infinity divided by a finite number is still infinity" sense, as numerical infinity is still able to be expressed as the result of an infinite sum. A Tier 0, under these proposals, necessarily cannot be the result of any sum, on account of its lack of substantial distinction.