We analysed the optical and radio properties of lobe-dominated giant-sized (>0.72 Mpc) radio quasars and compared the results with those derived for a sample of smaller radio sources to determine whether the large size of some extragalactic radio sources is related to the properties of their nuclei. We compiled the largest (to date) sample of giant radio quasars, including 24 new and 21 previously known objects, and calculated a number of important parameters of their nuclei such as the black hole mass and the accretion rate. We conclude that giant radio quasars have properties similar to those of smaller size and that giant quasars do not have more powerful central engines than other radio quasars. The results obtained are consistent with evolutionary models of extragalactic radio sources, which predict that giant radio quasars could be more evolved (aged) sources compared with smaller radio quasars. In addition we found out that the environment may play only a minor role in the formation of large-scale radio structures.