Methods of remotely, selectively controlling the flow rate of fluid moving through a subsea pipeline during dewatering of the pipeline involve a control unit of a subsea valve actuation system selectively, autonomously varying the flow of fluid through a fluid flow conduit of the system fluidly coupled to the pipeline at the pig receiving end thereof based at least partially upon one or more signals emitted by at least one pressure transducer or flow meter fluidly coupled to the fluid flow conduit.