  Let $Q$ be a quiver, $M$ a representation of $Q$ with an ordered basis $\cB$
and $\ue$ a dimension vector for $Q$. In this note we extend the methods of
\cite{L12} to establish Schubert decompositions of quiver Grassmannians
$\Gr_\ue(M)$ into affine spaces to the ramified case, i.e.\ the canonical
morphism $F:T\to Q$ from the coefficient quiver $T$ of $M$ w.r.t.\ $\cB$ is not
necessarily unramified.
  In particular, we determine the Euler characteristic of $\Gr_\ue(M)$ as the
number of \emph{extremal successor closed subsets of $T_0$}, which extends the
results of Cerulli Irelli (\cite{Cerulli11}) and Haupt (\cite{Haupt12}) (under
certain additional assumptions on $\cB$).
