Background <p>Cells contain membraneless organelles that have been proposed to form via phase separation involving dense networks of multivalent intermolecular interactions. As it is notoriously difficult to experimentally distinguish punctate structures formed by phase separation from those formed by other mechanisms, this issue is controversial. To complement experimental assays, we present a computational by-the-numbers approach to phase separation. We mine publicly available datasets to perform a molecular census of prominent subnuclear organelles in mouse embryonic stem cells: nucleoli, transcriptional condensates, heterochromatin foci, and Polycomb bodies. We estimate copy numbers and intermolecular distances and compare the latter to the Debye length, which is the characteristic distance over which intermolecular interactions typically occur.</p> Results <p>We find that none of the organelles studied here contain any protein species that shows intermolecular distances below the estimated Debye length if molecules in the organelles are randomly distributed, which disfavors the classical one-component phase separation scenario. Considering multiple species based on databases of phase-separating proteins, we find that nucleoli and transcriptional condensates are compatible with multi-component phase separation driven by proteins and RNAs, while heterochromatin foci and Polycomb bodies are better explained by a model in which proteins bind to chromatin without phase-separating via dense multivalent interaction networks. We also provide an interactive tool that allows testing of alternative multi-component scenarios.</p> Conclusion <p>We introduce a computational by-the-numbers approach to benchmark different demixing models that may explain the assembly of membraneless organelles. Our results suggest that cells use different mechanisms to form subnuclear organelles with different biophysical properties.</p>