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In this talk we consider several new developments on
strong connectivity questions in graphs.
For a fixed multigraph $H$, possibly containing loops, with
$V(H) = \{ h_1, \ldots , h_k \}$, we say a graph $G$ is $H$-linked
if for every choice of $k$ vertices $v_1 , \ldots, v_k$ in $G$,
there exists a subdivision of $H$ in $G$ such that $v_i$ represents
$h_i$ (for all $i$).  Using a $k$-matching as the graph $H$,
we obtain the well-known idea of a $k$-linked graph.
An $H$-immersion in $G$ is similar to $H$-linkage, except
that the paths in $G$, playing the role of the edges of $H$, are
only required to be edge disjoint.
We determine minimum degree conditions
for a graph $G$ to contain an $H$-linkage. We further generalize these
results to find conditions for a graph $G$ to contain an
$H$-immersion with a bounded number
of vertex repetitions on any choice of $k$ vertices.
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