Very massive primordial stars (140 M _⊙ < M < 260 M _⊙ ) are supposed to end their lives as PISN. Such an event can be traced by a typical chemical signature in low metallicity stars, but at the present time, this signature is lacking in the extremely metal-poor stars we are able to observe. Does it mean that those very massive objects were not formed, contrarily to the primordial star formation scenarios ? Could it be possible that they avoided this tragic fate ?

We explore the effects of rotation, anisotropical mass loss and magnetic field on the core size of very massive Population III models. We find that magnetic fields provide the strong coupling that is lacking in standard evolution metal-free models and our 150 M _⊙ Population III model avoids indeed the pair-instability explosion.