Drop impact on a wedged structure is a common phenomenon in daily life and industry. Although drop impact has been studied extensively since high-speed cameras have become available, little is known about drop impact on wedge tips of these structures. Here, we combine experiments and volume-of-fluid simulations to determine how velocity, the sharpness of the structure, and the surface wettability influence the outcome. The central impact of water drops onto wedge tips coated with superhydrophobic nanofilaments or with hydrophobic polystyrene (PS) was imaged. On superhydrophobic surfaces, drops fully rebound or split after impact. On hydrophobic PS surfaces, drops are deposited or split. A critical Weber number (We) was used to describe the transition between deposition/rebounding and splitting. It increases with the top width of the wedge tip and its top angle. The critical We and drop behavior is also affected by wetting properties which determine the drop adhesion and lateral drop friction. Our investigations may help to design new structures to prevent icing or produce tiny drops efficiently in applications.