The spoke instability in an E × B Penning discharge is shown to be strongly affected by the boundary that is perpendicular to B field lines. The instability is the strongest when bounded by dielectric walls. With a conducting wall, biased to collect electron current from the plasma, the spoke becomes faster, less coherent, and localized closer to the axis. The corresponding anomalous cross-field transport is assessed via simultaneous time-resolved measurements of plasma potential and density. This shows a dominant large-scale E × B anomalous character of the electron cross-field current for dielectric walls reaching 40%–100% of the discharge current, with an effective Hall parameter βeff ∼ 10. The anomalous current is greatly reduced with the conducting boundary (characterized by βeff ∼ 102). These experimental measurements are shown to be qualitatively consistent with the decrease in the E field that triggers the collisionless Simon-Hoh instability.