One of the difficulties with black is that it can be produced on any of the five e alleles and can be produced by different combinations of black enhancers. Karen is correct in that the basic pigment of black is dominant, however, one also can have black as a recessive as with the Blue gene. In addition some researchers have found a group of genes tentatively called 'rb 'or recessive black. Generally the recessive alleles do/can have some affect when heterozygous. An all black or nearly all black bird likely has black enhances that account for the coloration. I don't think that black can be accounted for with a single gene other than with the Blue alleles which is the recessive occurrence
Dave
Edit Getting back to Mottle - it is the Mottle gene that gives the white tipped feathers on the desired MF pattern. Mottle inhibits the production of pigments on the feather, in this case just at the feather tip when non hysterical Mottle (normal Mottle) is used.
		
		
	 
actually, what you're referring to are multiple loci for different mutations...  black blue splash and lavender (self blue) are all based on E (extended black) and the bbs and lavender genes simply modify the expression of the color (eumelanin inhibitors).  there may also be eumelanin enhancers as well, but that will just vary the depth of the color in certain areas (the melanizing gene causes a much darker hackle markings in blues, for example).
 
and blue is not a recessive gene. it's also dominant...   the primary recessive gene common in recognized cochin varieties is mottled. the e-locus genes have varying degrees of dominance, but E is the most dominant, followed by ER (birchen), eWh (wheaten), eb (partridge - not to be confused with the partridge variety of cochins, which involves the pattern gene), then e+ which is the wild type (duckwing).
 
so a mottled bird is typically E/E mo/mo.  E is capable of masking some other mutations, so breeding an E bird with a non-E bird isn't always predictable. the E (again, extended black) is NOT capable of masking mottled, barred or the eumelanin restrictors like blue/splash and self blue (aka lavender).  dun/khaki(incompletely dominant, much like blue/splash) and chocolate (sex-linked recessive) may also fall under the eumelanin restrictors, but i'm not too familiar with those mutations personally.
 
as regarding the calico/mille fleur cochins, the basis of the variety is mottled, with added columbian. individually, the genes express one way but when you start combining mutations, you sometimes get exaggerated or entirely different results.  like i was saying, since mille fleur already includes the columbian gene, to get the 'hysterical' calico, it's quite possible that the Db gene may also be involved, since it's also a columbian-like restrictor.