A least squares regression interval mapping model was derived to detect quantitative trait loci (QTL) with a unique mode of genomic imprinting, polar overdominance (POD), under a breed cross design model in outbred mammals. Tests to differentiate POD QTL from Mendelian, paternal or maternal expression QTL were also developed. To evaluate the power of the POD models and to determine the ability to differentiate POD from non-POD QTL, phenotypic data, marker data and a biallelic QTL were simulated on 512 F2 offspring. When tests for Mendelian versus parent-of-origin expression were performed, most POD QTL were classified as partially imprinted QTL. The application of the series of POD tests showed that more than 90% and 80% of medium and small POD QTL were declared as POD type. However, when breed-origin alleles were segregating in the grand parental breeds, the proportion of declared POD QTL decreased, which was more pronounced in a mating design with a small number of parents ($F_0$ and $F_1$). Non-POD QTL, i.e. with Mendelian or parent-of-origin expression (complete imprinting) inheritance, were well classified (>90%) as non-POD QTL, except for QTL with small effects and paternal or maternal expression in the design with a small number of parents, for which spurious POD QTL were declared.