  We present an extensive gallium NMR study of the geometrically frustrated
kagome bi-layer compound SrCr_(9p)Ga_(12-9p)O_(19) (Cr^3+, S=3/2) over a broad
Cr-concentration range (.72<p<.95). This allows us to probe locally the kagome
bi-layer susceptibility and separate the intrinsic properties due to the
geometric frustration from those related to the site dilution. Our major
findings are: 1) The intrinsic kagome bi-layer susceptibility exhibits a
maximum in temperature at 40-50 K and is robust to a dilution as high as ~20%.
The maximum reveals the development of short range antiferromagnetic
correlations; 2) At low-T, a highly dynamical state induces a strong wipe-out
of the NMR intensity, regardless of dilution; 3) The low-T upturn observed in
the macroscopic susceptibility is associated to paramagnetic defects which stem
from the dilution of the kagome bi-layer. The low-T analysis of the NMR
lineshape suggests that the defect can be associated with a staggered
spin-response to the vacancies on the kagome bi-layer. This, altogether with
the maximum in the kagome bi-layer susceptibility, is very similar to what is
observed in most low-dimensional antiferromagnetic correlated systems; 4) The
spin glass-like freezing observed at T_g=2-4 K is not driven by the
dilution-induced defects.
