A wrapping apparatus, its components, and corresponding methods for wrapping a load in packaging material are described herein. The apparatus has a packaging material dispenser having a frame and a plurality of packaging material supplies. The apparatus also has a load press for wrapping an upper surface of the load, where the load press has a central press section and a peripheral press section which can disengage the upper surface to allow wrapping of at least a part thereof. The apparatus also has an enclosure to prevent access during operation, as well as a packaging material seeking assembly which seeks out the packaging material to be wrapped. The apparatus and methods described allow for an automatic wrapping of a load which minimizes operator intervention, and further allow for the automatic resupply of packaging material.