  Following up on previous studies, we here complete a full analysis of the
void size distributions of the Cosmic Void Catalog (CVC) based on three
different simulation and mock catalogs; dark matter, haloes and galaxies. Based
on this analysis, we attempt to answer two questions: Is a 3-parameter
log-normal distribution a good candidate to satisfy the void size distributions
obtained from different types of environments? Is there a direct relation
between the shape parameters of the void size distribution and the
environmental effects? In an attempt to answer these questions, we here find
that all void size distributions of these data samples satisfy the 3-parameter
log-normal distribution whether the environment is dominated by dark matter,
haloes or galaxies. In addition, the shape parameters of the 3-parameter
log-normal void size distribution seem highly affected by environment,
particularly existing substructures. Therefore, we show two quantitative
relations given by linear equations between the skewness and the maximum tree
depth, and variance of the void size distribution and the maximum tree depth
directly from the simulated data. In addition to this, we find that the
percentage of the voids with nonzero central density in the data sets has a
critical importance. If the number of voids with nonzero central densities
reaches greater and or equal to 3.84 percentage in a simulation/mock sample,
then a second population is observed in the void size distributions. This
second population emerges as a second peak in the log-normal void size
distribution at larger radius.
