The combined processes of self-sputter (SS)-recycling and process gas recycling in high power impulse magnetron sputtering (HiPIMS) discharges are analyzed using the generalized recycling model (GRM). The study uses experimental data from discharges with current densities from the direct current magnetron sputtering range to the HiPIMS range, and using targets with self-sputter yields Y-SS from approximate to 0.1 to 2.6. The GRM analysis reveals that, above a critical current density of the order of J(crit) approximate to 0.2 A cm(-2), a combination of self-sputter recycling and gas-recycling is generally the case. The relative contributions of these recycling mechanisms, in turn, influence both the electron energy distribution and the stability of the discharges. For high self-sputter yields, above Y-SS approximate to 1, the discharges become dominated by SS-recycling, contain few hot secondary electrons from sheath energization, and have a relatively low electron temperature T-e. Here, stable plateau values of the discharge current develop during long pulses, and these values increase monotonically with the applied voltage. For low self-sputter yields, below Y-SS approximate to 0.2, the discharges above J(crit) are dominated by process gas recycling, have a significant sheath energization of secondary electrons and a higher T-e, and the current evolution is generally less stable. For intermediate values of YSS the discharge character gradually shifts between these two types. All of these discharges can, at sufficiently high discharge voltage, give currents that increase rapidly in time. For such cases we propose that a distinction should be made between unlimited runaway and limited runaway: in unlimited runaway the current can, in principle, increase without a limit for a fixed discharge voltage, while in limited runaway it can only grow towards finite, albeit very high, levels. For unlimited runway Y-SS amp;gt; 1 is found to be a necessary criterion, independent of the amount of gas-recycling in the discharge.