Velocity independent plate heights were apparently first recognized for hydrodynamic chromatography columns, packed with nonporous, 115 micron glass beads which were run at reduced mobile phase velocities of 10 to 10,000. Hydrodynamic chromatography separates based on the tendency of small molecules (or particles) to associate with slower moving fluid streamlines near the surfaces of particles, compared to larger molecules which seek faster streamlines. Consequently, the larger molecules elute first. Velocity independent plate heights in liquid chromatography have also been observed for nonadsorbed solutes in particulate and fibrous stationary phases. These stationary phases have pores which exceed 10(-4) to 10(-5) cm in dimension. The flat plate height is attributed to flow in the channels formed by these large intraparticle spaces. The development of plate height expressions which represent dispersion at interstitial velocities above 10 cm/min are discussed. Explanations of the uncoupling of dispersion from eluent flow rate in continuous stationary phases, membranes, and gigaporous particles is shown to have their origins in the studies of distribution of particles and molecules in hydrodynamic chromatography columns, and to be adequately described by modifications of the van Deemter equation.