Monte Carlo computer simulations of single, flexible, self-avoiding chains on a cubic lattice have been performed upon conditions of increasing segment-segment cohesive energy (deteriorating solvent quality). The simulations spanned a wide range of chain lengths (20-10,000, i.e., up to molecular weights of a few millions) and cohesive energies (0.0-0.45k(B)T, i.e., from athermal to very poor solvents). The chain length dependence of the chain size in poor solvents was characterized by a wide plateau of almost null growth for intermediate chain lengths. This plateau was linked to the development of the incipient constant density core, while genuine power law dependence (1/3) was not reached even for the longest chains and poorest solvents simulated here. The mere appearance of a core required substantial chain lengths (higher than 1000; molecular weights of a few hundred thousands), while short chains underwent a gradual densification devoid of any qualitative changes in the density distribution. Sufficiently long chains became more but not quite spherical and under-went a reasonably sharp second order phase transition. The findings were generally in agreement with predictions of mean-field theory and with the use of the standard scaling variables, despite slight inconsistencies. Nevertheless, the results stress the fact that short chains never form a constant density core and that core-dominance on the globule's properties ("volume approximation") is only valid for extraordinarily long chains [molecular weight of 0(109)], an effect linked to the relatively diffuse nature of the surface layer and originating from chain connectivity in conjunction with spherical geometry. (c) 2006 Wiley Periodicals, Inc.