  We consider a rotating Bose-Einstein condensate confined in combined harmonic
and quartic traps, following recent experiments [V. Bretin, S. Stock, Y. Seurin
and J. Dalibard, cond-mat/0307464]. We investigate numerically the behavior of
the wave function which solves the three-dimensional Gross Pitaevskii equation.
When the harmonic part of the potential is dominant, as the angular velocities
$Omega$ increases, the vortex lattice evolves into a giant vortex. We also
investigate a case not covered by the experiments or the previous numerical
works: for strong quartic potentials, the giant vortex is obtained for lower
$Omega$, before the lattice is formed. We analyze in detail the three
dimensional structure of vortices.
