The dynamics of the transverse magnetization in the zero-temperature XX chain is studied with emphasis on fronts emerging from steplike initial magnetization profiles. The fronts move with fixed velocity and display a staircase like internal structure whose dynamic scaling is explored both analytically and numerically. The front region is found to spread with time subdiffusively with the height and the width of the staircase steps scaling as t(-1/3) and t(1/3), respectively. The areas under the steps are independent of time; thus the magnetization relaxes in quantized "steps" of spin flips.