A dry granulation process of molten slag, in particular molten slag generated by iron and steel processes, comprising at least the following steps: - preparing a container containing the molten slag in the liquid state to be treated; - overturning said container so as to spill the slag contained therein with a pre-established flow; - while the flow of slag is spilled from said container and before it comes into contact with other part of the apparatus, hitting the flow of spilled slag by means of a jet of gas generated by gas-flow generating means, so as to break the flow of spilled slag into small drops before said flow of slag comes in contact with other parts or surfaces of the apparatus, and pushing said drops of said flow of slag according to a trajectory having at least one component along the longitudinal direction away from said gas-flow generating means and from said container causing the cooling of said drops during their flight and the gradual solidification of the same into granules while they are in-flight; - collecting the cooled granules of slag in a collection and transporting system further comprising at least one step consisting in controlling and modifying the cooling time and/or rate of said drops/granules of said flow of slag in order to obtain granules of slag having the desired morphological characteristics by modifying the in-flight residence time of said drops/granules of said flow of slag pushed by said jet of air, said step for controlling and modifying the in-flight residence time of said drops/granules of said flow of slag comprises at least one step consisting of deflecting and/or stopping the movement of said drops/granules of said flow of slag pushed by said jet of air by means of deflection and/or stopping means of said flow in drops/granules said deflection means for deflecting and/or stopping said flow in drops/granules of slag are configured for intercepting said flow and causing the precipitation of said granules of slag in a predetermined area of said collection system for the collection and transporting of the cooled slag granules, characterized in that said deflection means for deflecting and/or stopping said flow in drops/granules comprise at least one plate or panel positioned at a point of said component along the longitudinal direction of said flow in drops/granules of slag being said at least one plate or panel movable along said longitudinal direction or being said container and gas-flow generating means mounted on a supporting structure movable at least along a direction parallel to that of the gas flow, said plate or panel is fixed or also movable. - preparing a container containing the molten slag in the liquid state to be treated; - overturning said container so as to spill the slag contained therein with a pre-established flow; - while the flow of slag is spilled from said container and before it comes into contact with other part of the apparatus, hitting the flow of spilled slag by means of a jet of gas generated by gas-flow generating means, so as to break the flow of spilled slag into small drops before said flow of slag comes in contact with other parts or surfaces of the apparatus, and pushing said drops of said flow of slag according to a trajectory having at least one component along the longitudinal direction away from said gas-flow generating means and from said container causing the cooling of said drops during their flight and the gradual solidification of the same into granules while they are in-flight; - collecting the cooled granules of slag in a collection and transporting system further comprising at least one step consisting in controlling and modifying the cooling time and/or rate of said drops/granules of said flow of slag in order to obtain granules of slag having the desired morphological characteristics by modifying the in-flight residence time of said drops/granules of said flow of slag pushed by said jet of air,