Theoretical models are developed for the sedimentation from the margins of a particle-laden, axisymmetric, turbulent, buoyant plume, in a still environment and for an axisymmetric turbulent momentum jet. The models assume that the mass of each individual size fraction of sediment carried in a parcel of fluid decreases exponentially with time. For relatively coarse particles, the fallout models predict that the sediment deposition beyond a distance r on the ground expressed in log units should decay linearly with distance away from the vent for the momentum jet and should decrease with r1/3 for the buoyant plume. The exponential decay constant J is proportional to the terminal fall velocity Vt of the particles in both cases and inversely proportional to the square root of the initial momentum flux M0 for the jet fallout (Jj∝VtM0-1/2) and to the third power of the initial buoyancy flux F0 for the plume fallout (Jp∝VtF0-1/3). Smaller particles are affected by reentrainment caused by the turbulent eddies sweeping ambient fluid back into the plume or jet and thus reincorporating some particles that were released from the flow at greater heights. This is taken into account by introducing a reentrainment coefficient, ϕ, into the theoretical models with the assumption that the coefficient has a constant value for a plume of given strength. In new experiments, fallout occurs from the margins of particle-laden, fresh water, buoyant jets, and plumes in a tank of salty water, and sedimentation is measured on the tank floor. Two experiments were weakly affected by reentrainment and show excellent agreement with the simple theory. For smaller particles and increasingly buoyant plumes and strong jets, particle reentrainment is important. The experimental data are fitted by the new reentrainment theory, confirming that values of the reentrainment coefficient are approximately constant for a given flow. A settling number, β, is defined as the ratio of the characteristic velocity of the jet or plume to the particle settling velocity. For β≥1, reentrainment seems to reach an equilibrium state for which the reentrainment coefficient is a constant of value 0.1 for jets and 0.4 for plumes, irrespective of flow strength or particle size. The plume experiments indicate that the value of the reentrainment coefficient is strongly dependent on plume strength and particle size for β slightly less than 1. The general principles of sedimentation from turbulent plumes and jets are applied to the fallout of pumice from volcanic eruption columns and of metalliferous particles from black smokers on the ocean floor. For volcanic eruptions, the results provide an explanation for the near vent overthickening of tephra fall deposits and imply that lithic and pumice fragments from small lapilli up to at least 1 m diameter blocks are efficiently reentrained into eruption columns. The size of particles reentrained in hydrothermal plumes is predicted to vary from less than 100 μm in weakly buoyant plumes up to over 1000 μm in megaplumes. ¿ American Geophysical Union 1996