  We consider gluonic contributions to the heavy flavor Wilson coefficients at
3-loop order in QCD with two heavy quark lines in the asymptotic region $Q^2
\gg m_{1(2)}^2$. Here we report on the complete result in the case of two equal
masses $m_1 = m_2$ for the massive operator matrix element $A_{gg,Q}^{(3)}$,
which contributes to the corresponding heavy flavor transition matrix element
in the variable flavor number scheme. Nested finite binomial sums and iterated
integrals over square-root valued alphabets emerge in the result for this
quantity in $N$ and $x$-space, respectively. We also present results for the
case of two unequal masses for the flavor non-singlet OMEs and on the scalar
integrals ic case of $A_{gg,Q}^{(3)}$, which were calculated without a further
approximation. The graphs can be expressed by finite nested binomial sums over
generalized harmonic sums, the alphabet of which contains rational letters in
the ratio $\eta = m_1^2/m_2^2$.
