The transition to turbulence of the flow in a straight pipe is numerically studied over a range of Reynolds number where turbulence begins to expand by puff splitting. Puff splitting presents itself as a stochastic two-step process. A splitting puff first emits a kind of chaotic pseudopod made of azimuthally localized streaky structures at the downstream (leading) laminar-turbulent interface. This structure then expands azimuthally as it detaches from the parent puff. Detachment results from a collapse of turbulence over the whole section of the tube. Once the process is achieved a new puff is born ahead.