  We study high temperature spin transport in a disordered Heisenberg chain in
the ergodic regime. By employing a density matrix renormalization group
technique for the study of the stationary states of the boundary-driven
Lindblad equation we are able to study extremely large systems (400 spins). We
find both a diffusive and a subdiffusive phase depending on the strength of the
disorder and on the anisotropy parameter of the Heisenberg chain. Studying
finite-size effects we show numerically and theoretically that a very large
crossover length exists that controls the passage of a clean-system dominated
dynamics to one observed in the thermodynamic limit. Such a large length scale,
being larger than the sizes studied before, explains previous conflicting
results. We also predict spatial profiles of magnetization in steady states of
generic nondiffusive systems.
