The influence of heterogeneous architecture of alluvial aquifers on non-Fickian transport is explored using the Monte Carlo approach. More than two thousand high-resolution hydrofacies models representing seven groups of alluvial settings are built to test the effects of varying facies proportions, mean length and its anisotropy ratio, juxtapositional tendencies, and sub-facies heterogeneity. Results show that the volumetric fraction (P(Z)) of floodplain layers classified by their thicknesses Z controls the non-Fickian tailing of tracer transport at late times. A simple quantitative relationship S_BTC≈S_P(Z)/2-1 is built based on a multi-rate mass transfer analysis, where S_BTC is the slope of the power-law portion of tracer breakthrough curve, and S_P(Z) denotes the slope of the power-law portion of the distribution of P(Z) which can be measured, e.g., in core logs. At early times, the mean length of hydrofacies affects the non-Fickian tailing by controlling the channeling of flow in high-permeability non-floodplain materials and the sequestration in surrounding low-permeability floodplain layers. The competition between channeling and sequestration generates complex pre-asymptotic features, including sublinear growth of plume mean displacement, superlinear growth of plume variance, and skewed mass distribution. Those observations of the influence of medium heterogeneity on tracer transport at early and late times may lead to development of nonlocal transport models that can be parameterized using measurable aquifer characteristics.