We develop descriptions of the key processes influencing tephra dispersal from strong volcanic plumes. These are characterized by the development of a subvertical eruption column in the atmosphere that forms a spreading current at a level of neutral buoyancy. We describe the propagation of the spreading current due to both gravity and wind advection using scaling arguments and a simplified geometry to model particle sedimentation in a windy as well as a wind‐free environment. New parameterizations are used to describe the wind field below the spreading current, particle aggregation, and particle density variations. We conducted a broad study to investigate the effects of these processes and made comparisons with field observations. The greatest variations resulted from wind advection below the spreading current, which shifts the plume‐corner mass accumulation and the position of transitions in fallout regimes downwind. Particle aggregation strongly depends on the initial grain‐size distribution and significantly affects deposit thinning, depending on the aggregate size and density, and on the relative amount of aggregating particles. Small aggregates can reproduce secondary maxima of mass accumulation when sedimenting in a wind field. Variation of particle density also affects the resulting thinning trend. The model provides acceptable reproduction of observations of the propagation of the spreading current (tested with the Plinian phase of the 18 May 1980 eruption of Mount St. Helens) and of observed thinning of tephra fallout deposits (tested with deposits from Mount St. Helens, 1980, Askja D 1875, Quizapú 1932, Minoan eruption, 3.6 ka B.P., Novarupta A, 1912 and Hudson, 1991).