The longitudinal transport problem (the current is applied parallel to some bias magnetic field) in type-II superconductors is analyzed theoretically. Based on analytical results for simplified configurations, and relying on numerical studies for general scenarios, it is shown that a remarkable inversion of the current flow in a surface layer may be predicted under a wide set of experimental conditions. Strongly inhomogeneous current density profiles, characterized by enhanced transport toward the center and reduced, or even negative, values at the periphery of the conductor, are expected when the physical mechanisms of flux depinning and consumption (via line cutting) are recalled. A number of striking collateral effects, such as local and global paramagnetic behavior, are predicted. Our geometrical description of the macroscopic material laws allows a pictorial interpretation of the physical phenomena underlying the transport backflow.

8 pages, 6 figures (Best quality pictures are available by author's contact)