  Using a numerically exact technique we study spin transport and the evolution
of spin-density excitation profiles in a disordered spin-chain with long-range
interactions, decaying as a power-law, $r^{-\alpha}$ with distance and
$\alpha<2$. Our study confirms the prediction of recent theories that the
system is delocalized in this parameters regime. Moreover we find that for
$\alpha>3/2$ the underlying transport is diffusive with a transient
super-diffusive tail, similarly to the situation in clean long-range systems.
We generalize the Griffiths picture to long-range systems and show that it
captures the essential properties of the exact dynamics.
