  We analytically and numerically study spin transport in a one-dimensional
Heisenberg model in linear-response regime at infinite temperature. It is shown
that as the anisotropy parameter Delta is varied spin transport changes from
ballistic for Delta<1 to anomalous at the isotropic point Delta=1, to diffusive
for finite Delta>1, ending up as a perfect isolator in the Ising limit of
infinite Delta. Using perturbation theory for large Delta a quantitative
prediction is made for the dependence of diffusion constant on Delta.
