The Atomic Decomposition of an ontology is a succinct representation of the logic-based modules in that ontology. Ultimately, it reveals the modular structure of the ontology. Atomic Decompositions appear to be useful for both user and non-user facing services. For example, they can be used for ontology comprehension and to facilitate reasoner optimisation. In this article we investigate claims about the practicality of computing Atomic Decompositions for naturally occurring ontologies. We do this by performing a replication study using an off-the-shelf Atomic Decomposition algorithm implementation on three large test corpora of OWL ontologies. Our findings indicate that (a) previously published empirical studies in this area are repeatable and verifiable; (b) computing Atomic Decompositions in the vast majority of cases is practical in that it can be performed in less than 30 seconds in 90% of cases, even for ontologies containing hundreds of thousands of axioms; (c) there are occurrences of extremely large ontologies (< 1% in our test corpora) where the polynomial runtime behaviour of the Atomic Decomposition algorithm begins to bite and computations cannot be completed within 12-hours of CPU time; (d) the distribution of number of atoms in the Atomic Decomposition for an ontology appears to be similar for distinct corpora.