In this work, we report on the growth of AlGaN nanostructures by the droplet epitaxy process. Initially, well-oriented vertical AlN nanorod clusters were grown on to c-plane sapphire substrates by Plasma Assisted Molecular Beam Epitaxy (PA-MBE). On top of these AlN nanorods an Al0.76Ga0.24N layer was deposited, followed by 40 pairs of Al0.76Ga0.24N/AlN Multiple Quantum Wells (MQWs). Spontaneously formed nanodots and nanowires were observed by Field Emission Scanning Electron Microscopy (FESEM) on the top planes of these vertical nanorod arrays. For nearly stoichiometric conditions, 20 nm diameter AlGaN nanodots were formed selectively at the step edges generated during step-flow growth. For growth under excess group III conditions, lateral nanowires were formed perpendicular to the edges of the vertical nanorods, with widths varying from 20 nm near the center to 70 nm at the edge for a length of ∼150 nm. An enhancement of at least 15 times was obtained in the Cathodoluminescence (CL) emission peak intensity (290 nm) from the top of the nanorod structures. We believe these spontaneously formed well-ordered nanodot and horizontal nanowire structures are generated by the sequential formation and Nitridation of metal nanodroplets on the growth surface. Their properties can be controlled by optimization of the deposition parameters by varying the surface diffusivity of Ga and Al adatoms.