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Experimental investigations on linear surface discharges in air at atmospheric pressure have shown three main regions displayed at the advancing tip of these discharges. Theoretical models of the evolution of the ionized medium along these three succeeding regions are now established. They show how the matching between the coronalike head of the negative gliding spark and the thermalized leader channel occurs via a turbulent plasma region of small dimensions, where the energy of the electrical field is transferred into ionization within a duration of about 10 ns.