We investigate the flow of liquids around solid surfaces in the inertial regime, a situation commonly encountered with the so-called "teapot effect", the annoying tendency for a liquid to trickle down the outside of a receptacle after pouring. We demonstrate that surface wettability is an unexpected key factor in controlling flow separation and trickling, the latter being completely suppressed in the limit of superhydrophobic substrates. This unforeseen coupling is rationalized in terms of an inertial-capillary adhesion framework, which couples inertial flows to surface wettability effects. This description of flow separation successfully captures the observed dependence on the various experimental parameters, wettability, flow velocity, solid surface edge curvature. As a further illustration of this coupling, a real-time control of flow separation is demonstrated using electrowetting for contact angle actuation.