- A recomposer, allowing connecting a plurality of designation peripherals (A, B, C) to the same central unit of a computer system and making them simultaneously usable, and including: - inputs (11A, 11B, 11C) for receiving, from each of the designation peripherals, when said designation peripheral is connected to said recomposer, data normally received by the central unit when said designation peripheral is directly connected to said central unit; - at least one output for emitting data to the central unit, when said recomposer is connected to said central unit; - digital processing means (12, 13, 15, 13C, 14C, 16) configured to transform the data received at the inputs (11A, 11B, 11C) of the recomposer into data outputted from the recomposer; said outputted data being compliant in content and in structure to data which would be emitted by a designation peripheral including a single active surface; said outputted data characterising individually, at each instant, on the single active surface, actions carried out with the designation peripherals (A, B, C), actions characterised by the data received as inputs (11A, 11B, 11C), said recomposer being characterised in that: the digital processing means include: - at least one analyser (13, 13C) configured to extract, from the data received as inputs (11A, 11B, 11C) from each of the designation peripherals connected to said recomposer, a table of variable data and descriptors of said designation peripheral; at least one configurator configured to define dimensions and position of an active surface (16A, 16B, 16C) associated with each of the designation peripherals connected to said recomposer in a coordinate system of the single active surface; - at least one controller for transforming variable data of the data received as inputs (11A, 11B, 11C) into variable data of the outputted data; - at least one conditioner configured to structure the data to be outputted in accordance with a communication protocol understood by the central unit to which the recomposer must be connected; and in that: the configurator, for each active surface (16A, 16B, 16C) associated with a designation peripheral connected to the recomposer, defines dimensions and a position in the single active surface of an area (16A', 16B', 16C') corresponding to said active surface associated with the designation peripheral by: - a scaling of an abscissa axis and of an ordinate axis of each active surface known in a coordinate system of said active surface to a coordinate system of the single active surface; - a position of a reference point of each active surface in the coordinate system of the single active surface. - inputs (11A, 11B, 11C) for receiving, from each of the designation peripherals, when said designation peripheral is connected to said recomposer, data normally received by the central unit when said designation peripheral is directly connected to said central unit; - at least one output for emitting data to the central unit, when said recomposer is connected to said central unit; - digital processing means (12, 13, 15, 13C, 14C, 16) configured to transform the data received at the inputs (11A, 11B, 11C) of the recomposer into data outputted from the recomposer; said outputted data being compliant in content and in structure to data which would be emitted by a designation peripheral including a single active surface; said outputted data characterising individually, at each instant, on the single active surface, actions carried out with the designation peripherals (A, B, C), actions characterised by the data received as inputs (11A, 11B, 11C), said recomposer being characterised in that: the digital processing means include: - at least one analyser (13, 13C) configured to extract, from the data received as inputs (11A, 11B, 11C) from each of the designation peripherals connected to said recomposer, a table of variable data and descriptors of said designation peripheral; at least one configurator configured to define dimensions and position of an active surface (16A, 16B, 16C) associated with each of the designation peripherals connected to said recomposer in a coordinate system of the single active surface; - at least one controller for transforming variable data of the data received as inputs (11A, 11B, 11C) into variable data of the outputted data; - at least one conditioner configured to structure the data to be outputted in accordance with a communication protocol understood by the central unit to which the recomposer must be connected; - at least one analyser (13, 13C) configured to extract, from the data received as inputs (11A, 11B, 11C) from each of the designation peripherals connected to said recomposer, a table of variable data and descriptors of said designation peripheral; at least one configurator configured to define dimensions and position of an active surface (16A, 16B, 16C) associated with each of the designation peripherals connected to said recomposer in a coordinate system of the single active surface; - at least one controller for transforming variable data of the data received as inputs (11A, 11B, 11C) into variable data of the outputted data; - at least one conditioner configured to structure the data to be outputted in accordance with a communication protocol understood by the central unit to which the recomposer must be connected; - a scaling of an abscissa axis and of an ordinate axis of each active surface known in a coordinate system of said active surface to a coordinate system of the single active surface; - a position of a reference point of each active surface in the coordinate system of the single active surface.