Organic- and carbon-based materials are attractive for spintronics because their small spin-orbit coupling and low hyperfine interaction is expected to give rise to large spin-relaxation times. However, the corresponding spin-relaxation length is not necessarily large when transport is via weakly interacting molecular orbitals. Here we use graphite as a model system and study spin transport in the direction perpendicular to the weakly bonded graphene sheets. We achieve injection of highly (75%) spin-polarized electrons into graphite nano-structures of 300-500 nm across and up to 17 nm thick, and observe transport without any measurable loss of spin information. Direct visualization of local spin transport in graphite-based spin-valve sandwiches also shows spatially uniform and near-unity transmission for electrons at 1.8 eV above the Fermi level.