Roaming electronic devices (4) are recharged on a flat recharging surface provided with wide contact zones, by using an adapter (3) which defines two electrically conductive terminals (B1, B2) of small section in an outer face (F2) of a strip of the adapter. For each device to be powered, provision is made:—to stick an inner face of the strip (B) against a face (6) of the device and engage a connector (20) in the device on the side of a bent part (21) of the strip;—to place the adapter between the device and the recharging surface to allow conduction from two of the contact zones, the terminals being spaced apart by a predetermined distance (c) very much greater than their section size; and to selectively supply contact zones with current, for these zones on which the two terminals bear to be in an operational state and allow the recharging via the adapter.
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