Even the tires fitted on an Aeroplane are also made of electrical conductive rubbers. You can observe some amount of smoke when an Aeroplane touches the runway on landing. This is because of the discharge of accumulated charge.
In an Aeroplane, it is only a single wire wiring which carries positive charge to all the systems and electrical units. The Aeroplane body functions as the negative path. This is why all parts of an Aeroplane are always connected with electrical bonding strips. This keeps the complete Aeroplane in a uniform level of charge and smooth flow of current without producing any spark.
The static charge accumulated during flying due the clouds, surging of fuels etc is discharged through static wicks fitted on the Aeroplane and any residual is grounded on landing through an Aarthing cable fitted on the landing gear.