  Most quasars are known to be radio quiet and according to the ``spin
paradigm'', which connects their radio-loudness with the value of the black
hole spin, they must harbor very slowly rotating black holes. On the other
hand, quasars are powered by accretion which tends to increase the spin of the
black hole. We show that the Blandford-Znajek mechanism is not efficient enough
to counteract the spinning up of black holes by an accretion disk, regardless
of the accretion rate. We establish conditions under which it is possible to
obtain low values of the black hole spin, in the scenario involving a sequence
of many accretion events with random angular momenta. Our results are used to
select possible evolutionary scenarios which can explain radio bimodality of
quasars in terms of the ``spin paradigm''.
