  We perform a study of the nonlinear clustering of matter in the late-forming
dark matter (LFDM) scenario in which dark matter results from the transition of
a nonminimally coupled scalar field from radiation to collisionless matter. A
distinct feature of this model is the presence of a damped oscillatory cutoff
in the linear matter power spectrum at small scales. We use a suite of
high-resolution N-body simulations to study the imprints of LFDM on the
nonlinear matter power spectrum, the halo mass and velocity functions and the
halo density profiles. The model largely satisfies high-redshift matter power
spectrum constraints from Lyman-$\alpha$ forest measurements, while it predicts
suppressed abundance of low-mass halos ($\sim 10^{9}-10^{10}$ h$^{-1}$
M$_\odot$) at all redshifts compared to a vanilla $\Lambda$CDM model. The
analysis of the LFDM halo velocity function shows a better agreement than the
$\Lambda$CDM prediction with the observed abundance of low-velocity galaxies in
the local volume. Halos with mass $M\gtrsim 10^{11}$ h$^{-1}$ M$_\odot$ show
minor departures of the density profiles from $\Lambda$CDM expectations, while
smaller-mass halos are less dense, consistent with the fact that they form
later than their $\Lambda$CDM counterparts.
