The effect of convective transport on the late stage growth of droplets in the presence of sedimentation and shear flow is analyzed. The high Peclet number limit (UR/D)much greater than 1 is considered, where U is the characteristic velocity, R is the radius of the; droplet, and D is the diffusion coefficient. The growth of the droplet depends on the boundary condition for the fluid velocity at the droplet interface, and two types of boundary conditions are considered. For a rigid interface, which corresponds to the interface between a solid and a fluid,the tangential velocity is zero and the normal velocity is equal to the velocity of the surface. For a mobile interface, which corresponds to an interface between two fluids, the tangential and normal velocities are continuous. These results indicate that the scaling relations for the critical radius are R-c(t)proportional to t((1/2)) for a sedimenting droplet with a rigid interface, R-c(t)proportional to t((2/3)) for a sedimenting droplet with a mobile interface, R-c(t)proportional to t((3/7)) for a droplet with a rigid interface in a simple shear flow, and R-c(t)proportional to t((1/2)) for a droplet with a mobile interface in a simple shear flow. The rate of droplet growth is enhanced by a factor of Pe((1/3)) for rigid interfaces and Pe((1/2)) for mobile interfaces.