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Summary form only given. Spatially extended degenerate cw optical parametric oscillators (DOPOs) are predicted to display a rich variety of spatio-temporal behaviour in two transverse dimensions. Typical examples are the dynamical scaling of phase domains, randomly distributed cavity solitons, formation of spatial patterns and optical turbulence. Many of these features can be difficult to observe in real devices since they require input energies which are too large. Here we show that in the case of a higher finesse for the pump field than for the signal field, complex spatio-temporal phenomena can move extremely close to the signal generation threshold thus making their experimental observation more feasible.