A theoretical model of clast fallout from convective eruption columns has been developed which quantifies how the maximum clast size dispersal is determined by column height and wind strength. An eruption column consists of a buoyant convecting region which rises to a height H B where the column density equals that of the atmosphere. Above H B the column rises further to a height H T due to excess momentum. Between H T and H B the column is forced laterally into the atmosphere to form an upper umbrella region. Within the eruption column, the vertical and horizontal velocity fields can be calculated from exprimental and theoretical studies and consideration of mass continuity. The centreline vertical velocity falls as a nearly linear function over most of the column's height and the velocity decreases as a gaussian function radially away from the centreline. Both column height and vertical velocity are strong functions of magma discharge rate. From calculations of the velocity field and the terminal fall velocity of clasts, a series of particle support envelopes has been constructed which represents positions where the column vertical velocity and terminal velocity are equal for a clast of specific size and density. The maximum range of a clast is determined in the absence of wind by the maximum width of the clast support envelope. The trajectories of clasts leaving their relevant support envelope at its maximum width have been modelled in columns from 6 to 43 km high with no wind and in a wind field. From these calculations the shapes and areas of maximum grain size contours of the air-fall deposit have been predicted. For the no wind case the theoretical isopleths show good agreement with the Fogo A plinian deposit in the Azores. A diagram has been constructed which plots, for a particular clast size, the maximum range normal to the dispersal axis against the downward range. From the diagram the column height (and hence magma discharge rate) and wind velocity can be determined. Historic plinian eruptions of Santa Maria (1902) and Mount St. Helens (1980) give maximum heights of 34 and 19 km respectively and maximum wind speeds at the tropopause of m/s and 30 m/s respectively. Both estimates are in good agreement with observations. The model has been applied to a number of other plinian deposits, including the ultraplinian phase of the A.D. 180 Taupo eruption in New Zealand which had an estimated column height of 51 km and wind velocity of 27 m/s.