(a) Mean area in the source plane for magnification by more than ﹩A﹩ by the BH alone, and by the BH and stars of an image in the inner ﹩2\theta _{\mathrm{E}\,}﹩, for ﹩\theta _{\mathrm{E}\,}=\theta _{\infty }﹩ and the stellar lens surface density model of eq. (11) with ﹩\alpha =\frac{3}{2}﹩ (see text for scaling to arbitrary ﹩\theta _{\mathrm{E}\,}﹩). The two vertical hash marks roughly indicate the maximal magnification possible for extended sources, a ﹩1\,R_{\odot }﹩ and a ﹩10\,R_{\odot }﹩ star at a distance of ﹩2R_{0}﹩. (b) The differential source area per annulus in the lens plane that is magnified by more than ﹩A﹩. The case of a BH and stars (full lines) is compared to the contribution from the BH alone (dashed lines) for three threshold values of ﹩A﹩.