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First, lets get the terminology correct. It is not a "split black" It is a "black split to lavender." The first colour term references the phenotype (actual appearance), "split to" is synonymous with "heterogygous (sometimes abbreviated "het") for." The last term is the gene that is present in a bird in a heterozygous form; meaning that the bird also possesses a different allele for the gene.
And yes, a black split to lav bred to a lavender will produce both lavenders and blacks split to lav. WIth small numbers of offspring, percentages are unlikely to be accurate, with large numbers it should be close to half and half.