Context : Carbon-enhanced metal poor stars ( CEMP ) form a significant proportion of the metal-poor stars , their origin is not well understood , and this carbon-enhancement appears in stars that exhibit different abundance patterns . Aims : Three very metal-poor C-rich turnoff stars were selected from the SDSS survey , observed with the ESO VLT ( UVES ) to precisely determine the element abundances . In turnoff stars ( unlike giants ) the carbon abundance has not been affected by mixing with deep layers and is therefore easier to interpret . Methods : The analysis was performed with 1D ( one dimensional ) LTE ( local thermodynamical equilibrium ) static model atmospheres . When available , non-LTE corrections were applied to the classical LTE abundances . The 3D ( three dimensional ) effects on the CH and CN molecular bands were computed using hydrodynamical simulations of the stellar atmosphere ( CO ^ { 5 } BOLD ) and are found to be very important . Results : To facilitate a comparison with previous results , only 1D abundances are used in the discussion . The abundances ( or upper limits ) of the elements enable us to place these stars in different CEMP classes . The carbon abundances confirm the existence of a plateau at A ( C ) = 8.25 for [ Fe / H ] \geq - 3.4 . The most metal-poor stars ( [ Fe / H ] < -3.4 ) have significantly lower carbon abundances , suggesting a lower plateau at A ( C ) \approx 6.5 . Detailed analyses of a larger sample of very low metallicity carbon-rich stars are required to confirm ( or refute ) this possible second plateau and specify the behavior of the CEMP stars at very low metallicity . Conclusions :