Prior work in paper I on the size distribution of the fragments in single fracture of a three-dimensional solid is extended to the two-dimensional case (that of a thin plate). The underlying physical assumptions are the two-dimensional analogs of those made in I. These assumptions yield directly the probabilityd&pgr; (c,a)of formation of a fragment with perimeter and area in the rangesctoc+dcandatoa+da, respectively, ase−RdRin the general case, withRlinear incanda. The derivation yielding this Poisson form requires no assumption on the shape of a fragment. The numberdv (c,a)of fragments with perimeter and area in the rangesctoc+dcandatoa+da, respectively, is evaluated as the product ofd&pgr; (c,a)by thea priorinumber of particles with these values ofcanda. The distribution functiondv (c,a)meets the necessary physical requirement that the fracture process conserve surface area independently of particle shape. By assuming that all fragments are geometrically similar, one can replaced&pgr; (c,a)anddv (c,a)by forms,&pgr;(x)dxandv(x)dx, respectively, which depend only on a mean linear dimensionxof a fragment. The moments of the distribution corresponding to the total number and total perimeter of the fragments are divergent; this anomaly is explained as the result of neglect of depletion of Griffith flaws.