  We study the connection between magnetization transport and magnetization
profiles in zero-temperature XX chains. The time evolution of the transverse
magnetization, m(x,t), is calculated using an inhomogeneous initial state that
is the ground state at fixed magnetization but with m reversed from -m_0 for
x<0 to m_0 for x>0. In the long-time limit, the magnetization evolves into a
scaling form m(x,t)=P(x/t) and the profile develops a flat part (m=P=0) in the
|x/t|< c(m_0) region. The flat region shrinks to zero if m_0->1/2 while it
expands with the maximum velocity, c_0=1, for m_0->0. The states emerging in
the scaling limit are compared to those of a homogeneous system where the same
magnetization current is driven by a bulk field, and we find that the
expectation values of various quantities (energy, occupation number in the
fermionic representation) agree in the two systems.
