  The existence of pulsars with spin period below one millisecond is expected,
though they have not been detected up to now. Their formation depends on the
quantity of matter accreted from the companion which, in turn, is limited by
the mechanism of mass ejection from the binary. Mass ejection must be
efficient, at least in some cases, in order to produce the observed population
of moderately fast spinning millisecond pulsars. First we demonstrate, in the
framework of the widely accepted recycling scenario, using a population
synthesis approach, that a significant number of pulsars with spin period below
one millisecond is expected. Then we propose that significant variations in the
mass-transfer rate may cause, in systems with orbital periods larger than 1 hr,
the switch-on of a radio pulsar whose radiation pressure is capable of ejecting
out of the system most of the matter transferred by the companion and prevent
any further accretion. We show how this mechanism could dramatically alter the
binary evolution since the mechanism that drives mass overflow from the inner
Lagrangian point is still active while the accretion is inhibited. Moreover we
demonstrate that the persistency of this ``radio ejection'' phase depends on
the binary orbital period, demonstrating that close systems (orbital periods
lower than 1 hr) are the only possible hosts for ultra fast spinning neutron
stars. This could explain why submillisecond pulsars have not been detected so
far, as current radio surveys are hampered by computational limitations with
respect to the detection of very short spin period pulsars in short orbital
period binaries.
