If the cosmic scatter in my model is zero, then I am essentially following the TC08 model exactly. There is no upper or lower envelope of EW values for a given mass profile of the halo. Just one curve.

cov_frac:0.0100000 ell_c: 1.00000 Significance:1.4538320e-19 D:0.94777800

cov_frac:0.100000 ell_c: 1.00000 Significance:1.1752003e-15 D:0.85333300

cov_frac:0.200000 ell_c: 1.00000 Significance:4.6867554e-11 D:0.72555600

cov_frac:0.300000 ell_c: 1.00000 Significance:8.3111776e-09 D:0.65333300

cov_frac:0.400000 ell_c: 1.00000 Significance:2.0814730e-05 D:0.52333300

cov_frac:0.500000 ell_c: 1.00000 Significance:0.0010673220 D:0.44111100

cov_frac:0.600000 ell_c: 1.00000 Significance:0.011778121 D:0.38000001

cov_frac:0.700000 ell_c: 1.00000 Significance:0.038453044 D:0.34444401

cov_frac:0.800000 ell_c: 1.00000 Significance:0.15768489 D:0.29333300

cov_frac:0.900000 ell_c: 1.00000 Significance:0.016071932 D:0.37111101

cov_frac:1.00000 ell_c: 1.00000 Significance:0.00072479580 D:0.45000001

The output from the KS test. It shows that even for cosmic scatter of zero, the worst fitting distributions are those at very low covering fraction, and the best ones are around fc=0.8 roughly.