||Three types of magnetic phase diagrams as a function of composition or pressure, f (z, p), are identified among Ce systems: I) with the ordering temperature T-ord --> 0 monotonously, followed by a narrow region where non-Fermi-liquid (NFL) behavior is observed; II) with T-ord vanishing at finite temperature, but followed by an extended NFL region, and III) where T-ord remains nearly constant. Among the analyzed systems intrinsic differences are found in the evolution of their respective properties, namely: in group-1 an increase of the density of excitations is observed below T-ord. In group-II the evanescense of T-ord(z, p) coincides with the extrapolation to zero of the magnetic free energy (DeltaG --> 0), and the existence of a reference function implying that T-K not equal f (z, p), whereas T-ord = f (z, p). Finally, group-III is also characterized by the evanescense of T-ord where DeltaG --> 0, but in this case T-ord not equal f (z, p) whereas T-K = f (z, p). The characteristics of each group are discussed and compared together with the different C-p(T)/T dependencies at T greater than or equal to T-ord and some related scalings, which allow to recognize a quasi-paramagnetic phase.