As Basit well points out, RAINC comes from the convective scheme while RAINNC comes from the microphysics scheme.
To run the model with the cumulus scheme turned off, you simply have to specify "0" in the cu_physics option in the &physics section of your namelist.input, for example a simulation with four domains, where the innermost two have a resolution higher than 10 km:
max_dom = 4
dx = 54000, 18000, 6000, 2000,
dy = 54000, 18000, 6000, 2000,
cu_physics = 1, 1, 0, 0,
When you do this, the RAINC for the two innermost domains is always ZERO, so that the only rainfall comes from RAINNC. In this case, the values of RAINNC without cumulus (of the two innermost domains) are slightly higher than the values of RAINNC with cumulus. Actually, when computing statistics (POD, FAR, RMSE, BIAS), not using cumulus in domains with resolution higher than 10 km yields better results than when using cumulus. Paper to come