  A. Borisov classified into finitely many series the set of isomorphism
classes of germs of toric $\Q$-factorial singularities, of fixed dimension and
with minimal log discrepancy over the special point bounded from below by a
fixed real number. We extend this classification to germs of toric Fano
fibrations, possibly not $\Q$-factorial. As an application, we verify in the
toric setting a conjecture proposed by V. V. Shokurov on the existence of
bounded complements.
