In recent years, good progress toward a better understanding and control of the plasma performance in reversed-field pinch devices has been made. These improvements consist both of the discovery of spontaneous plasma regimes, termed the quasi single helicity ͑QSH͒ regime, in which part of the plasma core is no longer stochastic, and of the development of techniques for active control of plasma instabilities. In this paper, a systematic study of spontaneous QSH in the EXTRAP T2R device ͓P. R. Brunsell, H. Bergsaker, M. Cecconello et al., Plasma Phys. Control. Fusion 43, 1457 ͑2001͔͒ is presented. In this device, QSH states can occur spontaneously and it is associated with magnetic and thermal structures. A statistical analysis to determine the most favorable experimental conditions to have a transition to the QSH regime will be presented. The results described here are useful to understand the underlying properties of QSH regimes in view of future applications of the QSH active control in EXTRAP T2R; they are also important to have a comparison with the QSH studied in other devices.