Anomalous transport in advection‐dominated convergent flow tracer tests can occurs due to small‐scale heterogeneities in aquifer hydraulic properties. These result in fluctuations of the groundwater velocity field and complex connectivity patterns between injection and extraction wells. While detailed characterization of heterogeneity is often not possible in practice, a proper understanding of what fundamental physical mechanisms can give rise to macroscopic behaviors that are measurable is essential for proper upscaling of solute transport processes. We analyze here how heavy‐tailed breakthrough curves can arise in radially convergent flow to a well. The permeability fields are three‐dimensional multi‐Gaussian fields with varying statistical geometry and degrees of heterogeneity. We consider transport of conservative tracers from multiple injection locations by varying distance and angle from the extraction well. Anomalous power law tailing in breakthrough curves is attributed to a variety of features including the initial vertical stratification of the solute that arises due to a flux‐weighted injection, the injection distance to the well relative to the depth of the aquifer, and the statistics of the heterogeneity field as defined by the correlation length and variance of the permeability. When certain conditions cooccur for a given injection, such as strong connectivity contrasts between aquifer layers, injection distances comparable to the horizontal heterogeneity integral scales, and large global variances, breakthrough curves tend to scale as a PL with unit slope at late time. These findings offer new insights to understand what physical processes must be understood to develop and choose appropriate upscaling approaches that might reproduce such anomalous transport in heterogeneous advection‐dominated systems.