  A graph $G$ is said to be $\preceq$-ubiquitous, where $\preceq$ is the minor
relation between graphs, if whenever $\Gamma$ is a graph with $nG \preceq
\Gamma$ for all $n \in \mathbb{N}$, then one also has $\aleph_0 G \preceq
\Gamma$, where $\alpha G$ is the disjoint union of $\alpha$ many copies of $G$.
A well-known conjecture of Andreae is that every locally finite connected graph
is $\preceq$-ubiquitous.
  In this paper we give a sufficient condition on the structure of the ends of
a graph~$G$ which implies that $G$ is $\preceq$-ubiquitous. In particular this
implies that the full grid is $\preceq$-ubiquitous.
