  A cyclic quotient singularity of type $p^2/pq-1$ ($0<q<p, (p,q)=1$) has a
smoothing whose Milnor fibre is a $\mathbb Q$HD, or rational homology disk
(i.e., the Milnor number is $0$) ([9], 5.9.1). In the 1980's, we discovered
additional examples of such singularities: three triply-infinite and six
singly-infinite families, all weighted homogeneous. Later work of Stipsicz,
Szab\'{o}, Bhupal, and the author ([7], [1]) proved that these were the only
weighted homogeneous examples. In his UNC PhD thesis (unpublished but available
at [2]), our student Jacob Fowler completed the analytic classification of
these singularities, and counted the number of smoothings in each case, except
for types $\mathcal W$, $\mathcal N$, and $\mathcal M$. In this paper, we
describe his results, and settle these remaining cases; there is a unique
$\mathbb Q$HD smoothing component except in the cases of an obvious symmetry of
the resolution dual graph. The method involves study of configurations of
rational curves on projective rational surfaces.
