  A graph operation that {\em contracts edges} is one of the fundamental
operations in the theory of graph minors. Parameterized Complexity of editing
to a family of graphs by contracting $k$ edges has recently gained substantial
scientific attention, and several new results have been obtained. Some
important families of graphs, namely the subfamilies of chordal graphs, in the
context of edge contractions, have proven to be significantly difficult than
one might expect. In this paper, we study the \textsc{$\cal F$-Contraction}
problem, where $\cal F$ is a subfamily of chordal graphs, in the realm of
parameterized approximation. Formally, given a graph $G$ and an integer $k$,
\textsc{ $\cal F$-Contraction} asks whether there exists $X \subseteq E(G)$
such that $G/X \in \cal F$ and $|X| \leq k$. Here, $G/X$ is the graph obtained
from $G$ by contracting edges in $X$. We obtain the following results for the
\textsc{ $\cal F$-Contraction} problem. $(1)$ We show that \textsc{Clique
Contraction} admits a polynomial-size approximate kernelization scheme
(\textsf{PSAKS}). $(2)$ We give a $(2+\epsilon)$-approximate polynomial kernel
for \textsc{Split Contraction} (which also implies a factor
$(2+\epsilon)$-\FPT-approximation algorithm for \textsc{ Split Contraction}).
Furthermore, we show that, assuming \textsf{ Gap-ETH}, there is no
$\left(\frac{5}{4}-\delta \right)$-\FPT-approximation algorithm for
\textsc{Split Contraction}. Here, $\epsilon, \delta>0$ are fixed constants.
$(3)$ \textsc{Chordal Contraction} is known to be \WTH. We complement this
result by observing that the existing \textsf{W[2]-hardness} reduction can be
adapted to show that, assuming \FPT $\neq$ \textsf{W[1]}, there is no
$F(k)$-\FPT-approximation algorithm for \textsc{Chordal Contraction}. Here,
$F(k)$ is an arbitrary function depending on $k$ alone.
