Abstract
A graph G is said to be ≼ -ubiquitous, where ≼ is the minor relation between graphs, if whenever Γ is a graph with nG ≼ Γ for all n ∈ N, then one also has ℵ0G ≼ Γ, where αG is the disjoint union of α many copies of G. A well-known conjecture of Andreae is that every locally finite connected graph is ≼ -ubiquitous. In this paper we give a sufficient condition on the structure of the ends of a graph G which implies that G is ≼ -ubiquitous. In particular this implies that the full-grid is ≼ -ubiquitous.