We consider multiple unmanned aerial vehicles (UAVs) at a common altitude serving as data collectors to a network of IoT devices. First, using a probabilistic line of sight channel model, the optimal assignment of IoT devices to the UAVs is determined. Next, for the asymptotic regimes of a large number of UAVs and/or large UAV altitudes, we propose closed-form analytical expressions for the optimal data rate and characterize the corresponding optimal UAV deployments. We also propose a simple iterative algorithm to find the optimal deployments with a small number of UAVs at high altitudes. Globally optimal numerical solutions to the general rate maximization problem are found using particle swarm optimization.