This study investigates connectivity in a small portion of the extremely heterogeneous aquifer at the Macrodispersion Experiment (MADE) site in Columbus, Mississippi. A total of 19 fully penetrating soil cores were collected from a rectangular grid of 4 m by 4 m. Detailed grain size analysis was performed on 5 cm segments of each core, yielding 1740 hydraulic conductivity (K) estimates. Three different geostatistical simulation methods were used to generate 3‐D conditional realizations of the K field for the sampled block. Particle tracking calculations showed that the fastest particles, as represented by the first 5% to arrive, converge along preferential flow paths and exit the model domain within preferred areas. These 5% fastest flow paths accounted for about 40% of the flow. The distribution of preferential flow paths and particle exit locations is clearly influenced by the occurrence of clusters formed by interconnected cells with K equal to or greater than the 0.9 decile of the data distribution (10% of the volume). The fraction of particle paths within the high‐K clusters ranges from 43% to 69%. In variogram‐based K fields, some of the fastest paths are through media with lower K values, suggesting that transport connectivity may not require fully connected zones of relatively homogenous K. The high degree of flow and transport connectivity was confirmed by the values of two groups of connectivity indicators. In particular, the ratio between effective and geometric mean K (on average, about 2) and the ratio between the average arrival time and the arrival time of the fastest particles (on average, about 9) are consistent with flow and advective transport behavior characterized by channeling along preferential flow paths.