A “decomp” is any process of dividing a thing into pieces. To be a valid decomposition, it must be shown that the pieces encompass the entire scope of the “parent”. It is important to assess any proposed decomposition process with respect to this criterion.
The details of any given decomposition process depend on the domain being considered, and on the objective of the exercise. See, for example, Functional Decomposition and Physical Decomposition.
The notion that a thing could be considered piecemeal, and that the relationships between the pieces could be understood, is the original meaning of the Greek word forming the basis of “analysis”. When applied to verbiage this is, in fact, the original meaning of “analyze” (i.e., “rhetorical analysis”).