  We organize the nilpotent orbits in the exceptional complex Lie algebras into
series using the triality model and show that within each series the dimension
of the orbit is a linear function of the natural parameter a=1,2,4,8,
respectively for f_4,e_6,e_7,e_8. We also obtain explicit representatives in a
uniform manner. We observe similar regularities for the centralizers of
nilpotent elements in a series and graded components in the associated grading
of the ambient Lie algebra. More strikingly, for a greater than one, the
degrees of the unipotent characters of the corresponding Chevalley groups,
associated to these series through the Springer correspondance are given by
polynomials which have uniform expressions in terms of a.
