The effects of growth temperature, growth rate and local growth position on the morphology of self-assembled InSb/GaAs quantum dots (QDs) on (0 0 1) Ge substrate are investigated. It is found that for low growth rates, anti-phase domain (APD) boundaries formed during the growth of GaAs on Ge can effectively act as the preferential nucleation position of InSb QDs. For high growth rates, InSb/GaAs QDs nucleate on both the APD boundary and the APD surface, leading to high density-InSb QDs. The QD morphologies on the APD boundary and the APD surface are distinctly different. The roles of growth rate and local growth position on the morphology of realized QDs are described. By varying the growth conditions, low density and locally aligned QDs as well as high density InSb QDs can be obtained.