In this talk we consider several new developments on strong connectivity questions
in graphs. For a fixed multigraph H, possibly containing loops, with vertices of H
  the set h_1, ... , h_k, we say a graph G is H-linked if for every choice of k
vertices v_1, ... , 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 determining 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.