  We develop a model for the outer gravitationally unstable regions of
accretion disks around massive black holes, for primeval or solar abundances.
First we study star formation and evolution in a purely gaseous marginally
unstable disk, and we show that unstable fragments should collapse rapidly and
give rise to protostars which accrete at a high rate, acquire a mass of a few
tens of Mo, and explode as supernovae, producing strong enriched outflows.
Second we assume that the whole mass transport is ensured by the supernovae
which induce a transfer of angular momentum. For a star formation rate
proportional to the growth rate of gravitational instability, we find solutions
for the gas and stellar densities where the gas is close to gravitational
instability, between 0.1 and 10 pc M(BH) =10**6 Mo, and between 1 and 100 pc
for M(BH)=10**8 Mo or larger, whatever the abundances, but for relatively low
accretion rates. For larger accretion rates the number of stars becomes so
large that they inhibit further star formation, and/or the rate of SN is so
high that they distroy the homogeneity and the marginal stability of the disk.
We postpone the study of this case. Besides the fact that the mechanism solves
the problem of mass transport in a region of where global instabilities do not
work, there are several consequences of this model: it can explain the high
velocity metal enriched outflows implied by Broad Absorption Lines in quasars,
it can account for a pregalactic enrichment, if black holes formed early,
finally it can trigger starbursts in the central regions of galaxies. A check
of the model would be to detect a supernova exploding within a few parsecs from
the center of an AGN, an observation which can be performed in the near future.
