Several properties of massive stars with large effects of rotation and radiation are studied .
For stars with shellular rotation , i.e .
stars with a constant angular velocity \Omega on horizontal surfaces ( cf .
Zahn [ 1992 ] ) , we show that the equation of stellar surface has no significant departures with respect to the Roche model ; high radiation pressure does not modify this property .
Also , we note that contrarily to some current expressions , the correct Eddington factors \Gamma in a rotating star explicitely depend on rotation .
As a consequence , the maximum possible stellar luminosity is reduced by rotation .

We show that there are 2 roots for the equation giving the rotational velocities at break–up : 1 ) The usual solution , which is shown to apply when the Eddington ratio \Gamma of the star is smaller than formally 0.639 .
2 ) Above this value of \Gamma , there is a second root , inferior to the first one , for the break–up velocity .
This second solution tends to zero , when \Gamma tends towards 1 .
This second root results from the interplay of radiation and rotation , and in particular from the reduction by rotation of the effective mass in the local Eddington factor .
The analysis made here should hopefully clarify a recent debate between Langer ( [ 1997 , 1998 ] ) and Glatzel ( [ 1998 ] ) .

The expression for the global mass loss–rates is a function of both \Omega and \Gamma , and this may give raise to extreme mass loss–rates ( \Omega \Gamma –limit ) .
In particular , for O–type stars , LBV stars , supergiants and Wolf–Rayet stars , even slow rotation may dramatically enhance the mass loss rates .
Numerical examples in the range of 9 to 120 M _ { \odot } at various T _ { \mathrm { eff } } are given .

Mass loss from rotating stars is anisotropic .
Polar ejection is favoured by the higher T _ { \mathrm { eff } } at the polar caps ( g _ { \mathrm { eff } } –effect ) , while the ejection of an equatorial ring is favoured by the opacity effect ( \kappa –effect ) , if the opacity grows fastly for decreasing T _ { \mathrm { eff } } .