The axial part of the Z decay rate into hadrons ($\G^A_Z$) gets
extra singlet contributions due to the huge splitting between top
and bottom quark masses. By treating the axial neutral current in
the large top-mass limit we partially re-derive in a systematic manner
the known results on the contribution of the $\as^2$ order anomalous
"double triangle" diagrams to $\G^A_Z$ and resolve an ambiguity
concerning the scale at which the strong coupling constant
$\alpha_s$ is to be taken in these diagrams.
We evaluate and sum all
leading log and next to leading log QCD corrections of orders
$\as^{1+n}(\ln(M_Z/4m^2_t))^n$ and $\as^{2+n}(\ln(M_Z/4m^2_t))^n$
respectively.
We examine the sensitivity of our results to a change of
the renormalization scales to estimate the size of yet unknown
corrections of order $\alpha_s^3$ to $\G^A_Z$. The analysis implies
that the corrections might change the magnitude of the singlet
term by up to 30\% while they hardly might be of noticeable
numerical significance in comparison with the total contribution from
non-singlet terms.