The rotation of stars has many interesting and important consequences for the
photometric and chemical evolution of galaxies. Many of the predictions of
models of stellar rotation are now compared with observations of surface
abundances and velocities, with interferometric studies of fast rotating stars,
with internal rotation profiles as they can be deduced by asteroseismology, to
cite just a few observational constraints. In this paper, we investigate how
the outputs of models depend on the prescriptions used for the diffusion
coefficients included in the shellular rotating models. After recalling the
various prescriptions found in the literature, we discuss their impacts on the
evolutionary tracks and lifetimes of the Main-Sequence (MS) phase, the changes
of the surface composition and velocities during the MS phase, the distribution
of the core helium lifetime in the blue and the red part of the HR diagram, the
extensions of the blue loops, the evolution of the angular momentum of the
core, and the synthesis of primary nitrogen in fast-rotating metal-poor massive
stars. While some of these outputs depend only slightly on the prescriptions
used (for instance, the evolution of the surface velocities), most of them show
a significant dependence. The models which best fit the changes of the surface
abundances are those computed with the vertical shear diffusion coefficient of
Maeder (1997) and the horizontal shear diffusion coefficient by Zahn (1992).Comment: 19 pages, 4 figures, to appear in "SeIsmology for studies of stellar
Rotation and Convection", Lecture Notes in Physics (Springer Verlag, Berlin),
M.J. Goupil, K. Belkacem, C. Neiner, F. Ligni\`eres, and J. J. Green (eds