  Primordial black holes (PBHs) form from large-amplitude initial density
fluctuations and may comprise some or all of the dark matter. If PBHs have a
broadly extended mass spectrum, or in mixed PBH-particle dark matter scenarios,
the extreme density fluctuations necessary to produce PBHs also lead to the
formation of a much greater abundance of dark matter minihaloes that form
during the radiation epoch with internal densities potentially of order
$10^{12}$ M$_\odot$ pc$^{-3}$. We develop an analytic description of the
formation of these ultradense haloes and use it to quantitatively compare PBH
and halo distributions. PBHs that contribute only a per cent level fraction of
the dark matter are accompanied by ultradense haloes that nevertheless comprise
an order-unity fraction. These haloes would consist of either particle dark
matter or much smaller PBHs. This finding significantly alters the predictions
of many PBH scenarios, enabling a variety of new observational tests.
