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.
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