A system for use with a subterranean well can include a deployment apparatus configured to deploy one or more plugging devices into a fluid flow. The plugging devices are conveyed into the well by the fluid flow. The deployment apparatus can include multiple queues, different numbers of the plugging devices being contained in respective different ones of the queues. A method of deploying plugging devices can include connecting multiple queues of the plugging devices to a conduit, and deploying the plugging devices from a selected combination of the queues into the conduit. In another system, each of the plugging devices may include a body, and lines or fibers extending outwardly from the body.