We present the seafloor morphology and shallow seismic structure of the continental slope south-east of the Balearic promontory and of the adjacent Algero-Balearic abyssal plain from multibeam and chirp sonar data. The main purpose of this research was to identify the sediment pathways from the Balearic promontory to the Algero-Balearic deep basin from the Early Pliocene to the Present. The morphology of the southern Balearic margin is controlled by a SW-NE structural trend, whose main expressions are the Emile Baudot Escarpment transform fault, and a newly discovered WSW-ENE trend that affects the SW end of the escarpment and the abyssal plain. We relate the two structural trends to right-lateral simple shear as a consequence of the Miocene westward migration of the Gibraltar Arc. Newly discovered steep and narrow volcanic ridges were probably enabled to grow by local transtension along the transform margin. Abyssal plain knolls and seahills relate to the subsurface deformation of early stage halokinetic structures such as salt rollers, salt anticlines, and salt pillows. The limited thickness of the overburden and the limited amount of deformation in the deep basin prevent the formation of more mature halokinetic structures such as diapirs, salt walls, bulbs, and salt extrusions. The uppermost sediment cover is affected by a dense pattern of sub-vertical small throw normal faults resulting from extensional stress induced in the overburden by subsurface salt deformation structures. Shallow gas seismic character and the possible presence of an active polygonal fault system suggest upward fluid migration and fluid and sediment expulsion at the seafloor through a probable mud volcano and other piercement structures. One large debris flow deposit, named Formentera Debris Flow, has been identified on the lower slope and rise of the south Formentera margin. Based on current observations, we hypothesize that the landslide originating the Formentera Debris Flow occurred in the Holocene, perhaps in historical times.