By modeling stationary, rotating and magnetized outflows, self-similar in the meridional direction, we show that magneto-centrifugally driven winds can either collimate into thin jets or expand into wider bipolar flows, depending on the energy input into the flow and on the pressure distribution across the jet. The asymptotic analysis shows that overpressured winds, with respect to their environment, are radially expanding unless the central object is a Fast Magnetic Rotator (FMR), in which case the strong magnetic pinch collimates the outflow. Conversely underpressured winds are always cylindrically collimated. However they can be either magnetically focalized in a thin jet, as in the case of FMR, or less efficiently confined by the external pressure, appearing as bipolar flows in the case of Slow Magnetic Rotators (SMR). We can draw out a scenario for the evolution of cylindrically collimated jets into winds as the central star evolves from FMR to SMR, and wonder whether the solar wind itself is indeed a collimated bipolar outflow on large scales.