  A common mechanism to form primordial black holes in the early universe is by
enhancing at small-scales the scalar perturbations generated during inflation.
If these fluctuations have a large enough amplitude, they may collapse into
primordial black holes upon horizon re-entry. Such primordial black holes may
comprise the totality of the dark matter. We offer some considerations about
the formation and clustering of primordial black holes when the scalar
perturbations are characterised by a broad spectrum. Using the excursion set
method, as well as the supreme statistics, we show that the cloud-in-cloud
phenomenon, for which small mass primordial black holes may be absorbed by
bigger mass ones, is basically absent. This is due to the fact that the
formation of a primordial black hole is an extremely rare event. We also show
that, from the point of view of mass distribution, broad and narrow spectra
give similar results in the sense that the mass distribution is tilted towards
a single mass. Furthermore, we argue that primordial black holes from broad
spectra are not clustered at formation, their distribution is dominantly
Poissonian.
