A simple graph
$G=(V,E)$ admits an
$H$ -covering if every edge in
$E$ belongs to at least one subgraph of
$G$ isomorphic to a given graph
$H$ . Then the graph
$G$ is
$(a,d)$ -
$H$ -antimagic if there exists a bijection
$f:V\cup E\rightarrow \{1,2,\ldots ,|V|+|E|\}$ such that, for all subgraphs
$H^{\prime }$ of
$G$ isomorphic to
$H$ , the
$H^{\prime }$ -weights,
$wt_{f}(H^{\prime })=\sum _{v\in V(H^{\prime })}f(v)+\sum _{e\in E(H^{\prime })}f(e)$ , form an arithmetic progression with the initial term
$a$ and the common difference
$d$ . When
$f(V)=\{1,2,\ldots ,|V|\}$ , then
$G$ is said to be super
$(a,d)$ -
$H$ -antimagic. In this paper, we study super
$(a,d)$ -
$H$ -antimagic labellings of a disjoint union of graphs for
$d=|E(H)|-|V(H)|$ .