To accrete or not to accrete: the dilemma of the recycling scenario

We study the evolution of a low-mass X-ray binary by cou- pling a binary stellar evolution code with a general relativistic code that describes the behaviour of the neutron star. We find that non- conservative mass transfer scenarios are required to prevent the formation of submillisecond pulsars and/or the collapse to a black hole. We discuss the sweeping effects of an active magneto-dipole rotator on the transferred matter as a promising mechanism to obtain highly non-conservative evo- lutions.