  Lov\'{a}sz and Cherkassky discovered independently that, if $G$ is a finite
graph and $T\subseteq V(G)$ such that the degree $d_G(v)$ is even for every
vertex $v\in V(G)\setminus T$, then the maximum number of edge-disjoint paths
which are internally disjoint from~$T$ and connect distinct vertices of $T$ is
equal to $\frac{1}{2} \sum_{t\in T}\lambda_G(t, T\setminus \{t\})$ (where
$\lambda_G(t, T\setminus \{t\})$ is the size of a smallest cut that separates
$t$ and $T\setminus\{t\}$). From another perspective, this means that for every
vertex $t\in T$, in any optimal path-system there are $\lambda_G(t, T\setminus
\{t\})$ many paths between $t$ and~$T\setminus\{t\}$. We extend the theorem of
Lov\'{a}sz and Cherkassky based on this reformulation to all locally-finite
infinite graphs and their ends. In our generalisation, $T$ may contain not just
vertices but ends as well, and paths are one-way (two-way) infinite when they
establish a vertex-end (end-end) connection.
