  A $\mathbb Q$-conic bundle germ is a proper morphism from a threefold with
only terminal singularities to the germ $(Z \ni o)$ of a normal surface such
that fibers are connected and the anti-canonical divisor is relatively ample.
We obtain the complete classification of $\mathbb Q$-conic bundle germs when
the base surface germ is singular. This is a generalization of our previous
paper math/0603736, which further assumed that the fiber over $o$ is
irreducible.
