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
$d=E(H)V(H)$
.