  It is well-known that in finite graphs, large complete minors/topological
minors can be forced by assuming a large average degree. Our aim is to extend
this fact to infinite graphs. For this, we generalise the notion of the
relative end degree, which had been previously introduced by the first author
for locally finite graphs, and show that large minimum relative degree at the
ends and large minimum degree at the vertices imply the existence of large
complete (topological) minors in infinite graphs with countably many ends.
