Heritability estimates with a microsatellite parentage assignment based pedigree are of special interest in common carp cultured under traditional pond conditions. This method reduces common environment effects as all families can be grown immediately after hatching mixed in the same pond. We applied this method to study genetics of growth and processing traits in common carp at market size (1.5 kg and more). The experimental progeny was established by crossing 147 two-year old males and 8 females (six to eight-year old) of Hungarian synthetic mirror carp population. The fish grew up through three vegetation seasons and at the end a sample of 331 fish was examined for biometrical traits (standard length, body weight, relative head length, relative body height, relative body width), percent fat and processing traits (% processed body, % fillets with skin, % fillets without skin). It was shown that sex had a significant effect on most traits: females were larger and fatter than males, and they had both higher percent processed body and percent fillet with skin. Standard length, body weight, percent fat and relative head length had a high heritability (> 0.5), while relative body height, relative body width, percent processed body and fillet yields had a medium heritability (0.2–0.5). We found relatively high positive genetic correlations between body size (standard length and body weight) and percent fat (0.71 and 0.59, respectively), favourable genetic correlations between body size and percent processed body (0.69 for standard length and 0.74 for body weight) and between body size and fillet yields (0.50–0.77). Genetic correlations between body size and body shape (relative head length, relative body height and relative body width) were weak to moderate, thus selection for better growth should have little impact towards more rotund shape. Relative head length had strong negative correlation (− 0.7 to − 0.9) with percent fat, percent processed body and percent fillet yields. This means that indirect selection for reduced relative head length should be effective in improving of fillet yield.