For s-polypropylene, three different s-poly(propene-co-octene)s, two poly(ethylene-co-octene)s and poly(-caprolactone) we determined the relationships between the crystallization temperature Tc, the crystal thickness dc and the melting peak temperature Tf by carrying out time- and temperature-dependent small-angle x-ray scattering experiments. As a general law, dc is found to be inversely proportional to the supercooling below a characteristic temperature, Tc, which is always located above the equilibrium melting point following from an application of the Gibbs-Thomson equation. Tc is not (for the polypropylene-based copolymers) or only weakly (for the polyethylene-based copolymers) dependent on the co-unit content. The `crystallization line' Tc versus dc-1 and the Gibbs-Thomson melting line Tf versus dc-1 limit the range of the accessible partially crystalline states. The occurrence of two well defined independent boundary lines may be understood as indicating that the transformation from the melt into the partially crystalline state is generally, for homopolymers and copolymerized derivatives likewise, a two-step process, beginning with the building up of an initial form of lower order at the crystallization line which then becomes stabilized to end up in the state with layer-like morphology melting at Tf. Stabilization is achieved without a change in dc. AFM and TEM observations suggest that the initial structure could be composed of crystal blocks in planar assemblies. The stabilization then would result from their merging into a continuous lamella. It is proposed that the size of the blocks represents the minimum necessary to retain intrinsic stability. As a further result it was found that crystallinities reached at the end of isothermal crystallization processes remain invariant over larger ranges of Tc, in contrast to the changing length scales of the structure.