Carbon-enhanced metal-poor ( CEMP ) stars in the halo components of the Milky Way are explored , based on accurate determinations of the carbon-to-iron ( [ C/Fe ] ) abundance ratios and kinematic quantities for over 30000 calibration stars from the Sloan Digital Sky Survey ( SDSS ) . Using our present criterion that low-metallicity stars exhibiting [ C/Fe ] ratios ( ‘ ‘ carbonicity ’ ’ ) in excess of [ C/Fe ] = +0.7 are considered CEMP stars , the global frequency of CEMP stars in the halo system for [ Fe/H ] < -1.5 is 8 % ; for [ Fe/H ] < -2.0 it is 12 % ; for [ Fe/H ] < -2.5 it is 20 % . We also confirm a significant increase in the level of carbon enrichment with declining metallicity , growing from \langle [ C/Fe ] \rangle \sim + 1.0 at [ Fe/H ] = -1.5 to \langle [ C/Fe ] \rangle \sim + 1.7 at [ Fe/H ] = -2.7 . The nature of the carbonicity distribution function ( CarDF ) changes dramatically with increasing distance above the Galactic plane , | Z | . For | Z | < 5 kpc , relatively few CEMP stars are identified . For distances | Z | > 5 kpc , the CarDF exhibits a strong tail towards high values , up to [ C/Fe ] > +3.0 . We also find a clear increase in the CEMP frequency with | Z | . For stars with -2.0 < [ Fe/H ] < - 1.5 , the frequency grows from 5 % at | Z | \sim 2 kpc to 10 % at | Z | \sim 10 kpc . For stars with [ Fe/H ] < - 2.0 , the frequency grows from 8 % at | Z | \sim 2 kpc to 25 % at | Z | \sim 10 kpc . For stars with -2.0 < [ Fe/H ] < - 1.5 , the mean carbonicity is \langle [ C/Fe ] \rangle \sim + 1.0 for 0 kpc < | Z | < 10 kpc , with little dependence on | Z | ; for [ Fe/H ] < - 2.0 , \langle [ C/Fe ] \rangle \sim + 1.5 , again roughly independent of | Z | . Based on a statistical separation of the halo components in velocity space , we find evidence for a significant contrast in the frequency of CEMP stars between the inner- and outer-halo components – the outer halo possesses roughly twice the fraction of CEMP stars as the inner halo . The carbonicity distribution also differs between the inner-halo and outer-halo components – the inner halo has a greater portion of stars with modest carbon enhancement ( [ C/Fe ] \sim + 0.5 ] ) ; the outer halo has a greater portion of stars with large enhancements ( [ C/Fe ] \sim + 2.0 ) , although considerable overlap still exists . We interpret these results as due to the possible presence of additional astrophysical sources of carbon production associated with outer-halo stars , beyond the asymptotic giant-branch source that may dominate for inner-halo stars , with implications for the progenitors of these populations .