  We analyze the fractional quantization of the ballistic conductance
associated with the light and heavy holes bands in Si, Ge and GaAs systems. It
is shown that the formation of the localized hole state in the region of the
quantum point contact connecting two quasi-1D hole leads modifies drastically
the conductance pattern. Exchange interaction between localized and propagating
holes results in the fractional quantization of the ballistic conductance
different from those in electronic systems. The value of the conductance at the
additional plateaux depends on the offset between the bands of the light and
heavy holes, \Delta, and the sign of the exchange interaction constant. For
\Delta=0 and ferromagnetic exchange interaction, we observe additional plateaux
around the values 7e^{2}/4h, 3e^{2}/h and 15e^{2}/4h, while antiferromagnetic
interaction plateaux are formed around e^{2}/4h, e^{2}/h and 9e^{2}/4h. For
large \Delta, the single plateau is formed at e^2/h.
