In an automotive milling machine, comprising a machine frame, comprising a controller for the travelling and milling operation, comprising a working drum, comprising a transport conveyor, where the transport conveyor is slewable, relative to the machine frame, about a first axis extending essentially horizontally under an elevation angle, and sideways about a second axis extending orthogonally to the first axis under a slewing angle, where the transport conveyor discharges the milled material onto a loading surface of a transport vehicle at a specified conveying speed, and where the controller continuously controls positioning of the milled material automatically via, as a minimum, the slewing angle of the transport conveyor, it is provided for the following features to be achieved: the controller specifies and monitors limit values for a maximum permissible slewing angle range for slewing the transport conveyor variable in accordance with the current operating situation.