  Extended Abelian monopoles are investigated in SU(2) lattice gauge theory in
three dimensions. Monopoles are computed by Abelian projection in several
gauges, including the maximal Abelian gauge. The number $N_m$ of extended
monopoles in a cube of size $m^3$ (in lattice units) is defined as the number
of elementary ($1^3$) monopoles minus antimonopoles in the cube
($m=1,2,\ldots$). The distribution of $1^3$ monopoles in the nonlocal maximal
Abelian gauge is shown to be essentially random, while nonscaling of the
density of $1^3$ monopoles in some local gauges, which has been previously
observed, is shown to be mainly due to strong short-distance correlations. The
density of extended monopoles in local gauges is studied as a function of
$\beta$ for monopoles of fixed physical ``size'' ($m / \beta = {\rm fixed}$);
the degree of scale violation is found to decrease substantially as the
monopole size is increased. The possibility therefore remains that long
distance properties of monopoles in local gauges may be relevant to continuum
physics, such as confinement.
