In our studies of life‐supporting α‐1,3‐galactocyltransferase knockout (GalT‐KO) pig‐to‐baboon kidneys, we found that some recipients developed increased serum creatinine with growth of the grafts, without histological or immunological evidence of rejection. We hypothesized that the rapid growth of orthotopic pig grafts in smaller baboon recipients may have led to deterioration of organ function. To test this hypothesis for both kidneys and lungs, we assessed whether the growth of outbred (Yorkshire) organ transplants in miniature swine was regulated by intrinsic (graft) or extrinsic (host environment) factors. Yorkshire kidneys exhibited persistent growth in miniature swine, reaching 3.7 times their initial volume over 3 mo versus 1.2 times for miniature swine kidneys over the same time period. Similar rapid early growth of lung allografts was observed and, in this case, led to organ dysfunction. For xenograft kidneys, a review of our results suggests that there is a threshold for kidney graft volume of 25 cm3/kg of recipient body weight at which cortical ischemia is induced in transplanted GalT‐KO kidneys in baboons. These results suggest that intrinsic factors are responsible, at least in part, for growth of donor organs and that this property should be taken into consideration for growth‐curve–mismatched transplants, especially for life‐supporting organs transplanted into a limited recipient space. Factors intrinsic to transplanted organs play a role in subsequent growth of those organs, suggesting that this property should be considered for growth‐curve mismatched transplants, especially when transplanting life‐supporting organs into limited recipient space.