  We discuss the statistical properties of the volume of the nodal set of wave
function for two paradigmatic model systems which we consider in arbitrary
dimension $s\ge 2$: the cuboid as a paradigm for a regular shape with separable
wave functions, planar random waves as an established model for chaotic wave
functions in irregular shapes. We give explicit results for the mean and
variance of the nodal volume in arbitrary dimension, and for their limiting
distribution. For the mean nodal volume we calculate the effect of the boundary
of the cuboid where Dirichlet boundary conditions reduce the nodal volume
compared to the bulk. Boundary effects for chaotic wave functions are
calculated using random waves which satisfy a Dirichlet boundary condition on a
hyperplane. We put forward several conjectures what properties of cuboids
generalise to general regular shapes with separable wave functions and what
properties of random waves can be expected for general irregular shapes. These
universal features clearly distinct between the two cases.
