  The nature of structure formation around the particle free streaming scale is
still far from understood. Many attempts to simulate hot, warm, and cold dark
matter cosmologies with a free streaming cutoff have been performed with
cosmological particle-based simulations, but they all suffer from spurious
structure formation at scales below their respective free streaming scales --
i.e. where the physics of halo formation is most affected by free streaming. We
perform a series of high resolution numerical simulations of different WDM
models, and develop an approximate method to subtract artificial structures in
the measured halo mass function. The corrected measurements are then used to
construct and calibrate an extended Press-Schechter (EPS) model with sharp-$k$
window function and adequate mass assignment. The EPS model gives accurate
predictions for the low redshift halo mass function of CDM and WDM models, but
it significantly under-predicts the halo abundance at high redshifts. By taking
into account the ellipticity of the initial patches and connecting the
characteristic filter scale to the smallest ellipsoidal axis, we are able to
eliminate this inconsistency and obtain an accurate mass function over all
redshifts and all dark matter particle masses covered by the simulations. As an
additional application we use our model to predict the microhalo abundance of
the standard neutralino-CDM scenario and we give the first quantitative
prediction of the mass function over the full range of scales of CDM structure
formation.
