  We present a general recipe for constructing N-body realizations of galaxies
comprised of near-spherical and disc components. First, an exact spherical
distribution function for the spheroids (halo & bulge) is determined, such that
it is in equilibrium with the gravitational monopole of the disc components.
Second, an N-body realisation of this model is adapted to the full disc
potential by growing the latter adiabatically from its monopole. Finally, the
disc is sampled with particles drawn from an appropriate distribution function,
avoiding local-Maxwellian approximations. We performed test simulations and
find that the halo and bulge radial density profile very closely match their
target model, while they become slightly oblate due to the added disc gravity.
Our findings suggest that vertical thickening of the initially thin disc is
caused predominantly by spiral and bar instabilities, which also result in a
radial re-distribution of matter, rather than scattering off interloping
massive halo particles.
