The adsorption of dendrimers onto charged surfaces plays a role in many emerging applications. Numerous studies found in the literature report that dendrimers flatten at these interfaces. Here, we provide a simple scaling theory that describes the height of the adsorbed layer, the fraction of segments within the dendrimer that touch the surface, and the total number of dendrimers adsorbed as a function of generation of growth, surface charge density, and concentration. We demonstrate that these predictions agree well with extensive molecular dynamics simulations. Combined, the simulations and scaling argument indicate that simultaneous adsorption and compression at the interface take place.