  We study the continuum limit of the abelian string tension and the density of
abelian monopoles calculated after carefully fixing the maximal abelian gauge
by employing the simulated annealing algorithm. We present the evidence that
the abelian string tension converges to the nonabelian one in the continuum
limit. For the monopole density we confirm earlier findings that the density of
the properly defined infrared monopoles has correct scaling while the total
density seems divergent in the continuum limit due to ultraviolate
contributions. We also compare with results obtained with the usual iterative
gauge fixing algorithm.
