  Cold dark matter (CDM) could be composed of primordial black holes (PBH) in
addition to or instead of more orthodox weakly interacting massive particle
dark matter (PDM). We study the formation of the first structures in such
$\Lambda$PBH cosmologies using $N$-body simulations evolved from deep in the
radiation era to redshift 99. When PBH are only a small component of the CDM,
they are clothed by PDM to form isolated halos. On the other hand, when PBH
make most of the CDM, halos can also grow via clustering of many PBH. We find
that the halo mass function is well modelled via Poisson statistics assuming
random initial conditions. We quantify the nonlinear velocities induced by
structure formation and find that they are too small to significantly impact
CMB constraints. A chief challenge is how best to extrapolate our results to
lower redshifts relevant for some observational constraints.

Cosmology and Nongalactic Astrophysics