We apply halo abundance matching to obtain galaxy virial masses , M _ { h } , and radii , R _ { vir } , for 183 ‘ ‘ isolated ’ ’ galaxies from the ‘ ‘ Mg ii Absorber-Galaxy Catalog ’ ’ ( MAG ii CAT ) . All galaxies have spectroscopic redshifts ( 0.07 \leq z \leq 1.12 ) and their circumgalactic medium ( CGM ) is probed in Mg ii absorption within projected galactocentric distances D \leq 200 kpc . We examine the behavior of equivalent width , W _ { r } ( 2796 ) , and covering fraction , f _ { c } , as a function of D , D / R _ { vir } , and M _ { h } . Bifurcating the sample at the median mass \log M _ { h } / M _ { \odot } = 12 , we find : [ 1 ] systematic segregation of M _ { h } on the W _ { r } ( 2796 ) – D plane ( 4.0 ~ { } \sigma ) ; high-mass halos are found at higher D with larger W _ { r } ( 2796 ) compared to low-mass halos . On the W _ { r } ( 2796 ) – D / R _ { vir } plane , mass segregation vanishes and we find W _ { r } ( 2796 ) \propto ( D / R _ { vir } ) ^ { -2 } ( 8.9 ~ { } \sigma ) ; [ 2 ] high-mass halos have larger f _ { c } at a given D , whereas f _ { c } is independent of M _ { h } at all D / R _ { vir } ; [ 3 ] f _ { c } is constant with M _ { h } over the range 10.7 \leq \log M _ { h } / M _ { \odot } \leq 13.9 within a given D or D / R _ { vir } . The combined results suggest the Mg ii absorbing CGM is self-similar with halo mass , even above \log M _ { h } / M _ { \odot } \simeq 12 , where cold mode accretion is predicted to be quenched . If theory is correct , either outflows or sub-halos must contribute to absorption in high-mass halos such that low- and high-mass halos are observationally indistinguishable using Mg ii absorption strength once impact parameter is scaled by halo mass . Alternatively , the data may indicate predictions of a universal shut down of cold-mode accretion in high-mass halos may require revision .