  Unsustained matter distributions unescapely collapse unless fragmentation and
centrifugal or pressure support take place. Starting from the above evidence,
supermassive compact objects at the centre of large-mass galaxies are conceived
as the end-product of the gravitational collapse of local density maxima around
which overdensities are located. At the beginning of evolution, local density
maxima are idealized as homogeneous peaks, while the surrounding envelopes are
described by a power-law density profile. The dependence of the density profile
on a second parameter, chosen to be the ratio between peak and total mass, is
analysed. Overdensity evolution is discussed in the context of quintessence
cosmological models and further investigation is devoted to a special case with
the aim to describe the central collapse. An empirical relation between hole
and dark halo mass is translated into a dependence of the fractional hole mass
on the overdensity mass. Computations are performed up to the end of central
collapse, and density profiles of related configurations are determined
together with additional parameters. The central collapse is completed in early
times, no longer than a few hundredths of Gyr, which implies hole formation
when proto-haloes, proto-bulges, and proto-disks are still expanding or
contracting. No appreciable change in evolution is found with regard to
different mean peak heights related to equal masses. On the other hand, it is
recognized that homogeneous peaks collapse ``faster'' with respect to
surroundings envelopes, in low-mass than in large-mass overdensities. In
conclusion, it is inferred that gravitational collapse of homogeneous peaks
within overdensities may be a viable mechanism for hole generation.

Astrophysics