We present a new large-scale survey of the J=3–2 ^ { 12 } CO emission covering 4.8 square degrees around the Rosette Nebula . The results reveal the complex dynamics of the molecular gas in this region . We identify about 2000 compact gas clumps having a mass distribution given by dN / dM \sim M ^ { -1.8 } , with no dependence of the power law index on distance from the central O stars . A detailed study of a number of the clumps in the inner region show that most exhibit velocity gradients in the range 1–3 kms ^ { -1 } pc ^ { -1 } , generally directed away from the exciting nebula . The magnitude of the velocity gradient decreases with distance from the central O stars , and we compare the apparent clump acceleration with a photoionised gas acceleration model . For most clumps outside the central nebula , the model predicts lifetimes of a few 10 ^ { 5 } yrs . In one of the most extended of these clumps , however , a near-constant velocity gradient can be measured over 1.7 pc , which is difficult to explain with radiatively-driven models of clump acceleration . As well as the individual accelerated clumps , an unresolved limb-brightened rim lies at the interface between the central nebular cavity and the Rosette Molecular Cloud . Extending over 4 pc along the edge of the nebula , this region is thought to be at earlier phase of disruption than the accelerating compact globules . Blue-shifted gas clumps around the nebula are in all cases associated with dark absorbing optical globules , indicating that this material lies in front of the nebula and has been accelerated towards us . Red-shifted gas shows little evidence of associated line-of-sight dark clouds , indicating that the dominant bulk molecular gas motion throughout the region is expansion away from the O stars . In addition , we find evidence that many of the clumps lie in a molecular ring , having an expansion velocity of 30 km s ^ { -1 } and radius 11 pc . The dynamical timescale derived for this structure – \sim 10 ^ { 6 } yrs – is similar to the age of the nebula as a whole ( 2 \times 10 ^ { 6 } yrs ) . The J=3-2/1-0 ^ { 12 } CO line ratio in the clumps decreases with radial distance from the exciting O stars , from 1.6 at \sim 8 pc distance , to 0.8 at 20pc . This can be explained by a gradient in the surface temperature of the clumps with distance , and we compare the results with a simple model of surface heating by the central luminous stars . We identify 7 high-velocity molecular flows in the region , with a close correspondence between these flows and embedded young clusters or known young luminous stars . These flows are sufficiently energetic to drive gas turbulence within each cluster , but fall short of the turbulent energy of the whole GMC by two orders of magnitude . We find 14 clear examples of association between an embedded young star ( as seen by Spitzer at 24 \mu m ) and a CO clump in the molecular cloud facing the nebular . The CO morphology indicates that these are photo-evaporating circumstellar envelopes . CO clumps without evidence of embedded stars tend to have lower gas velocity gradients . It is suggested that the presence of the young star may extend the lifespan of the externally-photoevaporating envelope .