  The statistical production of antibaryons is considered within the canonical
ensemble formulation. We demonstrate that the antibaryon suppression in small
systems due to the exact baryon number conservation is rather different in the
baryon-free (B=0) and baryon-rich (B>1) systems. At constant values of
temperature and baryon density in the baryon-rich systems the density of the
produced antibaryons is only weakly dependent on the size of the system. For
realistic hadronization conditions this dependence appears to be close to
B/(B+1) which is in agreement with the preliminary data of the NA49
Collaboration for the antiproton/pion ratio in nucleus-nucleus collisions at
the CERN SPS energies. However, a consistent picture of antibaryon production
within the statistical hadronization model has not yet been achieved. This is
because the condition of constant hadronization temperature in the baryon-free
systems leads to a contradiction with the data on the antiproton/pion ratio in
e+e- interactions.
