  We aim to derive a simple analytic model to understand the essential
properties of vertically settling growing dust grains in laminar protoplanetary
discs. Separating the vertical dynamics from the motion in the disc midplane,
we integrate the equations of motion for both a linear and an exponential grain
growth rate. Numerical integrations are performed for more complex growth
models.
  We find that the settling efficiency depends on the value of the
dimensionless parameter gamma, which characterises the relative efficiency of
grain growth with respect to the gas drag. Since gamma is expected to be of
order as the initial dust-to-gas ratio in the disc (of order 10^-2), grain
growth enhances the energy dissipation of the dust particles and improve the
settling efficiency in protoplanetary discs. This behaviour is mostly
independent of the growth model considered as well as of the radial drift of
the particles.
