  We investigate contrasting behaviours emerging when studying foliations on
non-metrisable manifolds. It is shown that Kneser's pathology of a manifold
foliated by a single leaf cannot occur with foliations of dimension-one. On the
other hand, there are open surfaces admitting no foliations. This is derived
from a qualitative study of foliations defined on the long tube $\mathbb
S^1\times {\mathbb L}_+$ (product of the circle with the long ray), which is
reminiscent of a `black hole', in as much as the leaves of such a foliation are
strongly inclined to fall into the hole in a purely vertical way. More
generally the same qualitative behaviour occurs for dimension-one foliations on
$M \times {\mathbb L}_+$, provided that the manifold $M$ is "sufficiently
small", a technical condition satisfied by all metrisable manifolds. We also
analyse the structure of foliations on the other of the two simplest long pipes
of Nyikos, the punctured long plane. We are able to conclude that the long
plane $\mathbb L^2$ has only two foliations up to homeomorphism and six up to
isotopy.
