The effects of the finiteness of the physical domain over the free decay of homogeneous isotropic turbulence are explored in the present article. Saturation at the large scales is investigated by the use of theoretical analysis and eddy-damped quasi-normal Markovian calculations. Both analyses indicate a strong sensitivity of the large-scale features of the flow to saturation and finite Reynolds number effects. This aspect plays an important role in the general lack of agreement between grid turbulence experiments and numerical simulations. On the other hand, the statistical quantities associated with the behaviour of the spectrum in the inertial region are only marginally affected by saturation. These results suggest new guidelines for the interpretation of experimental and direct numerical simulation studies.