BACKGROUND In genomic prediction, it is common to centre the genotypes of single nucleotide polymorphisms based on the allele frequencies in the current population, rather than those in the base generation. The mean breeding value of non-genotyped animals is conditional on the mean performance of genotyped relatives, but can be corrected by fitting the mean performance of genotyped individuals as a fixed regression. The associated covariate vector has been referred to as a 'J-factor', which if fitted as a fixed effect can improve the accuracy and dispersion bias of sire genomic estimated breeding values (GEBV). To date, this has only been performed on populations with a single breed. Here, we investigated whether there was any benefit in fitting a separate J-factor for each breed in a three-way crossbred population, and in using pedigree-based expected or genome-based estimated breed fractions to define the J-factors. RESULTS For body weight at 7 days, dispersion bias decreased when fitting multiple J-factors, but only with a low proportion of genotyped individuals with selective genotyping. On average, the mean regression coefficients of validation records on those of GEBV increased with one J-factor compared to none, and further increased with multiple J-factors. However, for body weight at 35 days this was not observed. The accuracy of GEBV remained unchanged regardless of the J-factor method used. Differences between the J-factor methods were limited with correlations approaching 1 for the estimated covariate vector, the estimated coefficients of the regression on the J-factors, and the GEBV. CONCLUSIONS Based on our results and in the particular design analysed here, i.e. all the animals with phenotype are of the same type of crossbreds, fitting a single J-factor should be sufficient, to reduce dispersion bias. Fitting multiple J-factors may reduce dispersion bias further but this depends on the trait and genotyping rate. For the crossbred population analysed, fitting multiple J-factors has no adverse consequences and if this is done, it does not matter if the breed fractions used are based on the pedigree-expectation or the genomic estimates. Finally, when GEBV are estimated from crossbred data, any observed bias can potentially be reduced by including a straightforward regression on actual breed proportions.