In SU(2) lattice gauge theory in maximal center gauge, we investigate the d
ependence of center-projected Creutz ratios and the vortex density on latti
ce size and the number of gauge copies. The dependence on the number of cop
ies is rather strong on small lattices, but almost disappears on lattices s
ufficiently large compared to the expected average vortex thickness. The ce
nter-projected string tension, evaluated on sufficiently large lattices, is
in good agreement with the full asymptotic string tension, and the vortex
density scales according to the second-order asymptotic-freedom formula.