  We report on the theoretical study of the hole states in II-IV quantum dots
of a spherical and ellipsoidal shape, described by a smooth potential
confinement profiles, that can be modelled by a Gaussian functions in all three
dimensions. The universal dependencies of the hole energy, $g$-factor and
localization length on a quantum dot barrier height, as well as the ratio of
effective masses of the light and heavy holes are presented for the spherical
quantum dots. The splitting of the four-fold degenerate ground state into two
doublets is derived for anisotropic (oblate or prolate) quantum dots.
Variational calculations are combined with numerical ones in the framework of
the Luttinger Hamiltonian. Constructed trial functions are optimized by
comparison with the numerical results. The effective hole $g$-factor is found
to be independent on the quantum dot size and barrier height and is
approximated by simple universal expression depending only on the effective
mass parameters. The results can be used for interpreting and analyzing
experimental spectra measured in various structures with the quantum dots of
different semiconductor materials.
