The relationship between clade age and species richness has been increasingly used in macroevolutionary studies as evidence for ecologically versus time-dependent diversification processes. However, theory suggests that phylogenetic structure, age type (crown or stem age), and taxonomic delimitation can affect estimates of the age-richness correlation (ARC) considerably. We currently lack an integrative understanding of how these different factors affect ARCs, which in turn, obscures further interpretations. To assess its informative breadth, we characterize ARC behavior with simulated and empirical phylogenies, considering phylogenetic structure and both crown and stem ages. First, we develop a two-state birth-death model to simulate phylogenies including the origin of higher taxa and a hierarchical taxonomy to determine ARC expectations under ecologically and time-dependent diversification processes. Then, we estimate ARCs across various taxonomic ranks of extant amphibians, squamate reptiles, mammals, birds, and flowering plants. We find that our model reproduces the general ARC trends of a wide range of biological systems despite the particularities of taxonomic practice within each, suggesting that the model is adequate to establish a framework of ARC null expectations for different diversification processes when taxa are defined with a hierarchical taxonomy. ARCs estimated with crown ages were positive in all the scenarios we studied, including ecologically dependent processes. Negative ARCs were only found at less inclusive taxonomic ranks, when considering stem age, and when rates varied among clades. This was the case both in ecologically and time-dependent processes. Together, our results warn against direct interpretations of single ARC estimates and advocate for a more integrative use of ARCs across age types and taxonomic ranks in diversification studies.