The shape of impacting drops onto a solid surface is investigated by probing the local flow velocity and the local thickness profile of the spreading lamella during the drop impact. First, as a model situation of no viscous coupling between the liquid and the substrate, the impact of a drop onto hot plates, above the Leidenfrost temperature, is considered. In this case, we demonstrate that the velocity and thickness profiles are in good agreement with inviscid convective flow theory. This local description allows us to revisit the modelling of well-studied global behaviour such as drop spreading. Building from this idealized situation, viscous boundary-layer effects emerging from frictional coupling on a cold surface are then captured.