Method for the additive manufacture of a plurality of components on a manufacturing support plate by melting powder using at least one beam of energy, each component comprising at least two opposite front and rear frontal faces delimiting the thickness of the said component and protrusions projecting out from the front frontal face thereof, the method comprising the following steps: - a) simultaneous manufacture, by deposition and selective melting of layers of powder stacked on the manufacturing support plate, of a plurality of intermediate assemblies at least in one row, each intermediate assembly comprising: - a component produced at an inclined angle with respect to the manufacturing support plate and forming an angle of between 20° and 70° with the said support plate, - a support interposed between the manufacturing support plate and a lower base of the said component, and - at least one local supporting element resting against the rear frontal face of the component, the said local supporting element of the said assembly being arranged and configured in such a way as to avoid any contact with the protrusions of the component of the adjacent intermediate assembly of the row, - the fused powder layers of the component, of the support and of the said local supporting element being joined to one another during this manufacturing step, - b) formation, during the selective-melting phases of the manufacturing step, of rupture initiators in regions of connection of the support and of the said supporting element to the said component of each intermediate assembly, - c) separation of the component from the support and the said local supporting element of each intermediate assembly after the manufacturing step by breaking of the said connecting regions. - at least one groove is formed locally on the rear frontal face of the component of each intermediate assembly and/or on the lower base of the said component during the manufacturing step, the region of connection of the said local supporting element to the said component being positioned inside the said groove. - a) simultaneous manufacture, by deposition and selective melting of layers of powder stacked on the manufacturing support plate, of a plurality of intermediate assemblies at least in one row, each intermediate assembly comprising: - a component produced at an inclined angle with respect to the manufacturing support plate and forming an angle of between 20° and 70° with the said support plate, - a support interposed between the manufacturing support plate and a lower base of the said component, and - at least one local supporting element resting against the rear frontal face of the component, the said local supporting element of the said assembly being arranged and configured in such a way as to avoid any contact with the protrusions of the component of the adjacent intermediate assembly of the row, - the fused powder layers of the component, of the support and of the said local supporting element being joined to one another during this manufacturing step, - a component produced at an inclined angle with respect to the manufacturing support plate and forming an angle of between 20° and 70° with the said support plate, - a support interposed between the manufacturing support plate and a lower base of the said component, and - at least one local supporting element resting against the rear frontal face of the component, the said local supporting element of the said assembly being arranged and configured in such a way as to avoid any contact with the protrusions of the component of the adjacent intermediate assembly of the row, - the fused powder layers of the component, of the support and of the said local supporting element being joined to one another during this manufacturing step, - b) formation, during the selective-melting phases of the manufacturing step, of rupture initiators in regions of connection of the support and of the said supporting element to the said component of each intermediate assembly, - c) separation of the component from the support and the said local supporting element of each intermediate assembly after the manufacturing step by breaking of the said connecting regions. - at least one groove is formed locally on the rear frontal face of the component of each intermediate assembly and/or on the lower base of the said component during the manufacturing step, the region of connection of the said local supporting element to the said component being positioned inside the said groove. - at least one groove is formed locally on the rear frontal face of the component of each intermediate assembly and/or on the lower base of the said component during the manufacturing step, the region of connection of the said local supporting element to the said component being positioned inside the said groove.