The paper reports how experimental data from a fan-stirred explosion vessel have extended the boundary of the previously defined regime, within which stable premixed turbulent combustion occurs. It also defines the properties of the bordering regime of turbulent flame quenching. The combustion regime is defined by the normalised turbulent burning velocity, U, the Karlovitz stretch factor, K, and strain rate Markstein number, Masr. The data cover hydrogen, methane, and higher hydrocarbons, at different equivalence ratios and pressures. In contrast, the flame quench regime is defined by the mean diameters of flame kernels at quench, normalised by their laminar flame thickness, dk/δk. These values must be exceeded to initiate a propagating flame. Values of dk/δk increase with both K and Masr. It is also shown, that the flame extinction at blow-off of non-premixed jet flames, is closely related to the observed single kernel quenching of premixed flames. With jet flames, the flow number, U*, has similarities with K. The normalised jet burner diameters, Db/δk, change with U*, in a similar fashion to the way dk/δk changes with K for premixed flames. Finally, the way in which highly turbulent premixed flames can survive extinction by the entrainment of flame gases from a pilot flame is analysed.