Carbon-enhanced metal poor stars (CEMP) form a significant proportion of the metal-poor stars, their origin is not well understood. 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. The analysis was performed with 1D LTE static model atmospheres. When available, non-LTE corrections were applied to the classical LTE abundances. The 3D effects on the CH and CN molecular bands were computed using hydrodynamical simulations of the stellar atmosphere (CO5BOLD) and are found to be very important. 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] ≥ -3.4. The most metal-poor stars ([Fe/H] < -3.4) have significantly lower carbon abundances, suggesting a lower plateau at A(C) ≈ 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.