  We study a general class of problems called F-deletion problems. In an
F-deletion problem, we are asked whether a subset of at most $k$ vertices can
be deleted from a graph $G$ such that the resulting graph does not contain as a
minor any graph from the family F of forbidden minors.
  We obtain a number of algorithmic results on the F-deletion problem when F
contains a planar graph. We give (1) a linear vertex kernel on graphs excluding
$t$-claw $K_{1,t}$, the star with $t$ leves, as an induced subgraph, where $t$
is a fixed integer. (2) an approximation algorithm achieving an approximation
ratio of $O(\log^{3/2} OPT)$, where $OPT$ is the size of an optimal solution on
general undirected graphs. Finally, we obtain polynomial kernels for the case
when F contains graph $\theta_c$ as a minor for a fixed integer $c$. The graph
$\theta_c$ consists of two vertices connected by $c$ parallel edges. Even
though this may appear to be a very restricted class of problems it already
encompasses well-studied problems such as {\sc Vertex Cover}, {\sc Feedback
Vertex Set} and Diamond Hitting Set. The generic kernelization algorithm is
based on a non-trivial application of protrusion techniques, previously used
only for problems on topological graph classes.
