Using a scattering technique based on a parametrized linear combination of atomic orbitals Hamiltonian, we calculate the ballistic quantum conductance of multiwall carbon nanotubes. We find that interwall interactions not only block some of the quantum conductance channels, but also redistribute the current nonuniformly over individual tubes across the structure. Our results provide a natural explanation for the unexpected integer and noninteger conductance values reported for multiwall nanotubes by Stefan Frank et al. [Stefan Frank et al., Science 280, 1744 (1998)].