We demonstrate that aligned carbon-nanotube arrays are efficient transporters of laser-generated mega-ampere electron currents over distances as large as a millimeter. A direct polarimetric measurement of the temporal and the spatial evolution of the megagauss magnetic fields (as high as 120 MG) at the target rear at an intensity of (10(18)-10(19)) W/cm2 was corroborated by the rear-side hot electron spectra. Simulations show that such high magnetic flux densities can only be generated by a very well collimated fast electron bunch.