That language hosts a multiplicity of part-whole relations is largely accepted, but no complete formal account is currently available. We first show how most distinctions between part-whole relations can be explained by considering the ontological categories of the arguments. We then focus on "component-integral whole" (CIW), a most important but formally little-studied relation. The analysis of the functional concepts involved leads us to introduce lexical categories and to characterize a notion of functional dependence. On this basis, four cases of CIW are distinguished and formally defined. The contrastive acceptability of determinative compound nouns shows the linguistic relevance of these distinctions. Lastly, we show how the definitions provide a simple solution to the elusive issue of variable transitivity patterns.