  We study the problem of the Landau gauge fixing in the case of the SU(2)
lattice gauge theory. We show that the probability to find a lattice Gribov
copy increases considerably when the physical size of the lattice exceeds some
critical value $\approx2.75/\sqrt{\sigma}$, almost independent of the lattice
spacing. The impact of the choice of the copy on Green functions is presented.
We confirm that the ghost propagator depends on the choice of the copy, this
dependence decreasing for increasing volumes above the critical one. The gluon
propagator as well as the gluonic three-point functions are insensitive to
choice of the copy (within present statistical errors). Finally we show that
gauge copies which have the same value of the minimisation functional ($\int
d^4x (A^a_\mu)^2$) are equivalent, up to a global gauge transformation, and
yield the same Green functions.
