Abstract Ontology-based data access is concerned with the problem of querying incomplete data sources in the presence of an ontology. A key notion in this setting is that of ontology-mediated query, which is a database query coupled with an ontology. An interesting issue is whether the answer to an ontologymediated query can be computed by parallelizing it over the connected components of the database, i.e., whether the query distributes over components. This allows us to evaluate the query in a distributed and coordination-free manner. We investigate distribution over components for classes of ontologymediated queries where the database query is a conjunctive query and the ontology is formulated using existential rules. For each such class, we syntactically characterize its fragment that distributes over components, and we study the problem of deciding whether a query distributes over components.