We observe a transition of domain-wall (DW) dynamics in ferromagnetic wires made of Co/Ni multilayers by use of transport measurement. As the wire width reduces, DW dynamics exhibits a transition from dendrite growth to pure DW motion. The threshold width is found to be about 300 nm and strongly depends on the relative dragging direction of the magnetic field and the current on DW: parallel (antiparallel) direction results in much smaller (larger) threshold width. It should be considered as a building block for DW-motion-based device applications. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4733667]