  A Q-homology plane is a normal complex algebraic surface having trivial
rational homology. We classify singular Q-homology planes which are C^1- or
C*-ruled. We analyze their completions, the number of different rulings, the
number of affine lines on it and we give constructions. Together with
previously known results this completes the classification of Q-homology planes
with smooth locus of non-general type. We show also that the dimension of a
family of homeomorphic but non-isomorphic singular Q-homology planes having the
same weighted boundary, singularities and Kodaira dimension can be arbitrarily
big.
