  We investigated numerically the distribution of participation numbers in the
3d Anderson tight-binding model at the localization-delocalization threshold.
These numbers in {\em one} disordered system experience strong level-to-level
fluctuations in a wide energy range. The fluctuations grow substantially with
increasing size of the system. We argue that the fluctuations of the
correlation dimension, $D_2$ of the wave functions are the main reason for
this. The distribution of these correlation dimensions at the transition is
calculated. In the thermodynamic limit ($L\to \infty$) it does not depend on
the system size $L$. An interesting feature of this limiting distribution is
that it vanishes exactly at $D_{\rm 2max}=1.83$, the highest possible value of
the correlation dimension at the Anderson threshold in this model.
