Taxonomic membership frequencies exhibit distributions in which groups with few numbers of subtaxa are much more common in a clade than those with more subtaxa. Here, a “broken plate” model is developed to describe such taxonomic memberships; some higher taxonomic group (the plate) is randomly subdivided into intermediate taxonomic units (plate fragments), whose sizes are dependent on the number of taxonomic subunits that they each contain. Theoretical distributions of membership frequencies produced by this model yield a superior fit to data from both modern and fossil groups, as illustrated by classifications for primarily fossil brachiopods and entirely modern mammals. The nature of these distributions is consistent with the contention that Linnaean membership frequencies result from the random partitioning of taxonomic/morphologic space. Moreover, numbers of taxa contained within hierarchically equivalent groups are unrelated, as are membership numbers at taxonomically higher and lower levels of consideration. Agreement between observed taxonomic memberships and those anticipated from the random partitioning of diversity as described by the “broken plate” model bears directly on a number of fundamental questions including the significance of extreme polytypy and inferred causes of adaptive radiation within many taxonomic groups.