Within the framework of the AdS/CFT correspondence, we study the time evolution of an energetic R–current propagating through a finite temperature, strongly coupled, N = 4 SYM plasma and propose a physical picture for our results. In this picture, the current splits into a pair of massless partons, which then evolve via successive branchings, in such a way that energy is quasi–democratically divided among the products of a branching. We point out a duality between the transverse size of the partonic system produced through branching and the radial distance traveled by the dual Maxwell wave in the AdS geometry. For a time–like current, the branching occurs already in the vacuum, where it gives rise to a system of low– momentum partons isotropically distributed in the transverse plane. But at finite temperature, the branching mechanism is modified by the medium, in that the rate for parton splitting is enhanced by the transfer of transverse momentum from the partons to the plasma. This mechanism, which controls the parton energy loss, is sensitive to the energy density in the plasma, but not to the details of the thermal state. We compute the lifetime of the current for various kinematical regimes and provide physical interpretations for other, related, quantities, so like the meson screening length, the drag force, or the trailing string, that were previously computed via AdS/CFT techniques.