  Contractads are operadic-type algebraic structures well-suited for describing
configuration spaces indexed by a simple connected graph $\Gamma$.
Specifically, these configuration spaces are defined as
$\mathrm{Conf}_{\Gamma}(X):=X^{|V(\Gamma)|}\setminus \cup_{(ij)\in E(\Gamma)}
\{x_i=x_j\}$. In this paper, we explore functional equations for the Hilbert
series of Koszul dual contractads and provide explicit Hilbert series for
fundamental contractads such as the commutative, Lie, associative and the
little discs contractads.
  Additionally, we focus on a particular contractad derived from the wonderful
compactifications of $\mathrm{Conf}_{\Gamma}(\mathbb{k})$, for
$\mathbb{k}=\mathbb{R},\mathbb{C}$. First, we demonstrate that for complete
multipartite graphs, the associated wonderful compactifications coincide with
the modular compactifications introduced by Smyth. Second, we establish that
the homology of the complex points and the homology of the real locus of the
wonderful contractad are both quadratic and Koszul contractads. We offer a
detailed description of generators and relations, extending the concepts of the
Hypercommutative operad and cacti operads, respectively. Furthermore, using the
functional equations for the Hilbert series, we describe the corresponding
Hilbert series for the homology of modular compactifications.
