We describe results from a survey for J=3-2 ^ { 12 } CO emission from visible stars classified as having an infrared excess . The line is clearly detected in 21 objects , and significant molecular gas ( \geq 10 ^ { -3 } Jupiter masses ) is found to be common in targets with infrared excesses \geq 0.01 ( \geq 56 per cent of objects ) , but rare for those with smaller excesses ( \sim 10 per cent of objects ) . A simple geometrical argument based on the infrared excess implies that disc opening angles are typically \geq 12 \mbox { $ { } ^ { \circ } $ } for objects with detected CO ; within this angle , the disc is optically thick to stellar radiation and shields the CO from photodissociation . Two or three CO discs have an unusually low infrared excess ( \leq 0.01 ) , implying the shielding disc is physically very thin ( \leq 1 \mbox { $ { } ^ { \circ } $ } ) . Around 50 per cent of the detected line profiles are double-peaked , while many of the rest have significantly broadened lines , attributed to discs in Keplerian rotation . Simple model fits to the line profiles indicate outer radii in the range 30-300 au , larger than found through fitting continuum SEDs , but similar to the sizes of debris discs around main sequence stars . As many as 5 have outer radii smaller than the Solar System ( 50 au ) , with a further 4 showing evidence of gas in the disc at radii smaller than 20 au . The outer disc radius is independent of the stellar spectral type ( from K through to B9 ) , but there is evidence of a correlation between radius and total dust mass . Also the mean disc size appears to decrease with time : discs around stars of age 3-7 Myr have a mean radius \sim 210 au , whereas discs of age 7-20 Myr are a factor of 3 smaller . This shows that a significant mass of gas ( at least 2 \mathrm { M _ { \oplus } } ) exists beyond the region of planet formation for up to \sim 7 Myr , and may remain for a further \sim 10 Myr within this region . The only bona fide debris disc with detected CO is HD9672 ; this shows a double peaked CO profile and is the most compact gas disc observed , with a modelled outer radius of 17 au . In the case of HD141569 , detailed modelling of the line profile indicates gas may lie in two rings , with radii of 90 and 250 au , similar to the dust structure seen in scattered light and the mid-infrared . In both AB Aur and HD163296 we also find the sizes of the molecular disc and dust scattering disc are similar ; this suggests that the molecular gas and small dust grains are closely co-located .