We investigate the impact of a liquid droplet on a solid or liquid surface,modelled by the Navier Stokes equations in the gas and liquid phases.The equations are solved by discretizing the fields on an adaptive quadtree grid,using a projection method for the pressure,the time stepping and the incompressibility condition.The advection of the velocity fields is performed using the second-order Bell-Collela-Glaz scheme,and the viscosity is treated partially implicitly.The interface is tracked using a Volume of Fluid(VOF)method with a Mixed Youngs-Centered Scheme for the determination of the normal vector and a Lagrangian-Explicit scheme for VOF advection.Curvature is computed using the height-function method.Surface tension is computed from curvature by a well-balanced Continuous Surface Force method.Density and viscosity are computed from the VOF fraction C by an arithmetic mean.This arithmetic mean is followed by three steps iteration of an elementary filtering.This whole set of methods is programmed in the free Gerris flow solver.Some additional simulations are conducted in a different methodology,using the potential flow equations in the liquid and a lubrication model in the gas.We use these methods to study in axisymmetric geometry the fall of an initially spherical droplet on a solid surface.The droplet falls from a small height h0 above the liquid film or solid surface with a velocity V.At high velocity,gravity and surface tension effects are small.Then two regimes have been predicted in the literature one with the thickness of the air film h~V-1=2 and one with h~V-2=3.In terms of dimensionless numbers the expected scalings are h/D~St-1=2 and h/D~St-2=3.We try to discriminate between these two regimes with our numerical simulations.We also investigate the formation of an ejecta sheet or jet,which is found to occur either during the droplet skating or after contact of the droplet with the solid surface.The various regimes for ejecta sheet or jet formation are mapped as a function of the viscosity and density ratios of the carrier gas and droplet liquid.We hope to shed some light on the mechanism of the splash-deposition transition.