  We study spin transport in a boundary driven XXZ spin chain. Driving at the
chain boundaries is modeled by two additional spin chains prepared in
oppositely polarized states. Emergent behavior, both in the transient dynamics
and in the long-time quasi-steady state, is demonstrated. Time-dependent
matrix-product-state simulations of the system-bath state show ballistic spin
transport below the Heisenberg isotropic point. Indications of exponentially
vanishing transport are found above the Heisenberg point for low energy initial
states while the current decays asymptotically as a power law for high energy
states. Precisely at the critical point, non-ballistic transport is observed.
Finally, it is found that the sensitivity of the quasi-stationary state on the
initial state of the chain is a good witness of the different transport phases.
