  We use recent progress in simulating the production of magnetohydrodynamic
jets around black holes to derive the cosmic spin history of the most massive
black holes, with masses >~10^8 Msol. Assuming the jet efficiency depends on
spin a, we can approximately reproduce the observed `radio loudness' of quasars
and the local radio luminosity function. Using the X-ray luminosity function
and the local mass function of supermassive black holes, SMBHs we can reproduce
the individual radio luminosity functions of radio sources showing high- and
low-excitation narrow emission lines. The data favour spin distributions that
are bimodal, with one component around spin zero and the other close to maximal
spin. In the low-excitation galaxies, the two components have similar
amplitudes. For the high-excitation galaxies, the amplitude of the high-spin
peak is typically much smaller than that of the low-spin peak. A bimodality
should be seen in the radio loudness of quasars. We predict that the
low-excitation galaxies are dominated by SMBHs with masses >~10^8 Msol, down to
radio luminosity densities ~10^21 W Hz-1 sr-1 at 1.4~GHz. Our model is also
able to predict the radio luminosity function at z=1, and predicts it to be
dominated by high-excitation galaxies above luminosity densities >~10^26 W Hz-1
sr-1, in full agreement with the observations. From our parametrisation and
using the best fitting jet efficiencies there is marginal evidence for
evolution in spin: the mean spin increases slightly from <a>~0.25 at z=1 to
<a>~0.35 at z=0, and the fraction of SMBHs with a>=0.5 increases from
0.16+-0.03 at z=1 to 0.24+-0.09 at z=0. Our results are in excellent agreement
with the mean radiative efficiency of quasars, as well as recent cosmological
simulations. We discuss the implications in terms of accretion and SMBH
mergers, and galactic black holes (Abridged).
