In this paper we study the spin transport by using the spin-pumping effect in epitaxial magnetic single and double layer film structures. For the magnetic single layer sample we show the spin-pumping-induced interface damping increases and saturates with the Au capping layer thickness. In addition magnetic double layer structures allowed us to investigate both the spin-pump and spin-sink effects. Coupling of pure spin currents to the magnetization via spin-sink effect is studied using time-resolved magneto-optical Kerr effect. These measurements were used to study the propagation of pure spin currents across a Au spacer layer between the two ferromagnets. The propagation of spin momentum density through the Au spacer layer was well described by spin-diffusion equation, which takes into account electron momentum and spin-flip scattering. The spin-diffusion theory was integrated into modified Landau-Lifshitz equations accounting in self-consistent manner for spin-pump/sink mechanism and spin momentum density propagation. Good agreement between theory and experimental data was found.