The scientific and technical challenges involved in building the planar electrical connection of an atomic scale circuit to N electrodes (N > 2) are discussed. The practical, laboratory scale approach explored today to assemble a multi-access atomic scale precision interconnection machine is presented. Depending on the surface electronic properties of the targeted substrates, two types of machines are considered: on moderate surface band gap materials, scanning tunneling microscopy can be combined with scanning electron microscopy to provide an efficient navigation system, while on wide surface band gap materials, atomic force microscopy can be used in conjunction with optical microscopy. The size of the planar part of the circuit should be minimized on moderate band gap surfaces to avoid current leakage, while this requirement does not apply to wide band gap surfaces. These constraints impose different methods of connection, which are thoroughly discussed, in particular regarding the recent progress in single atom and molecule manipulations on a surface.