We describe the upscaled groundwater flow and solute transport characteristics of two-dimensional hydraulic conductivity fields with three fundamentally different spatial textures and consider the conditions under which physical mobile--immobile domain mass transfer occurs in these fields. All three fields have near-identical lognormal univariate conductivity distributions, as well as near-identical isotropic spatial covariance functions. They differ in the pattern by which high- or low-conductivity regions are connected: the first field has connected high-conductivity structures; the second is multivariate log-Gaussian and, hence, has connected structures of intermediate value; and the third has connected regions of low conductivity. We find substantially different flow and transport behaviors in the three different fields. Flow and transport in the multivariate log-Gaussian field are consistent with stochastic theory. The field with connected high-conductivity paths has an effective conductivity greater than the geometric mean and large variations in fluid velocity. It produces significant mass transfer behavior (i.e., tailing) when the conductivity variance is large and, depending on the system parameters, this mass transfer is driven by either diffusion or advection. In the field with connected low-conductivity regions, the effective conductivity is below the geometric mean and transport is well characterized by the advection--dispersion model with a dispersivity smaller than that in the multivariate log-Gaussian field. Thus, physical mobile--immobile domain mass transfer may occur in smooth hydraulic conductivity fields with univariate log-Gaussian density functions if the variability in conductivity is sufficient and the high values are more connected than modeled by the multivariate log-Gaussian distribution.