  Context. The lack of sub-Jovian planets on orbits of $P_{\rm orb} < 3$ days
is a puzzling aspect of galaxy formation with regard to the distribution of
exoplanets whose origins are currently unresolved. Aims. The possible
explanations behind the formation of the sub-Jovian or Neptunian desert include
several scenarios that can lead to different shapes for the boundary,
predicting various dependencies between the position of the boundary and the
stellar parameters. Methods. We explored the exoplanet distribution in various
2D and 3D projections, revealing the stellar-dependent substructures in the
$P_{\rm orb}-M_{P}$ and the $P_{\rm orb}-R_{P}$ parameter plane. Results. We
demonstrate that the upper boundary includes a range of planets, namely,
inflated hot Jupiters and normal hot Jupiters, in the two parameter planes,
respectively. We confirm the dependence of the boundary on several stellar
parameters and, based on a fuzzy clustering analysis, we provide quantitative
formulae for the dependencies in groups of smaller and larger planets. The
overall period-radius distribution shows chemical substructures as well, with
the boundary being dependent on volatiles and alpha-elements, alongside
marginal (to none) dependence found for refractory elements. Conclusions. These
findings confirm multiple plausible causes for the formation of the desert,
particularly preferring those scenarios related to the irradiation-driven loss
of the atmospheres of moderately massive planets as the predominant process in
shaping planetary distributions.
