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We present simulations of electronic transport in single-wall and multi-wall carbon nanotubes, which are placed between two metallic contacts. The carbon atoms are represented by a local pseudopotential, and a transfer-matrix technique is used to solve the Schrodinger equation. Results show that electrons continuously propagate in the shell in which they are initially injected, with transfers to other tubes hardly exceeding one percent of the whole current even when micron-long distances are considered. The conductance and repartition of the current are traced to the band structure of the nanotube. These simulations thus show that provided one can prepare the electrons to enter a given shell of multi-wall nanotubes, it may be possible to use them as independent conduction channels.