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

Growing dust grains in protoplanetary discs - III. Vertical settling