  We prove (i) a simple sufficient geometric condition for localisation of a
sequence of first Dirichlet eigenfunctions provided the corresponding Dirichlet
Laplacians satisfy a uniform Hardy inequality, and (ii) localisation of a
sequence of first Dirichlet eigenfunctions for a wide class of elongating
horn-shaped domains. We give examples of sequences of simply connected, planar,
polygonal domains for which the corresponding sequence of first eigenfunctions
with either Dirichlet, or Neumann, boundary conditions $\kappa$-localise in
$L^2$.
