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We consider a Bose-Einstein condensate (BEC) of $N$ atoms of repulsiveinteraction $\sim U_0$, in an elliptical trap, axially pierced by aGaussian-intensity laser beam, forming an effective (quasi-2D) toroidal trapwith minimum at radial distance $\rho = \rho_p$. The macroscopic angularmomentum states $\Psi_l(\rho,\theta) \sim \sqrt{N}\Phi_l(\rho) e^{i l \theta}$for integer $l$ spread up to $\rho \lesssim \rho_{max} \sim (NU_0)^{1/4} \gg\rho_p$. The spreading lowers rotational energies, so estimated lowmetastability barriers can support large $l \lesssim l_{max} \sim (NU_0)^{1/4},\lesssim 10$ for typical parameters. The $l$-dependent density profile$|\Phi_l(\rho)|^2 - |\Phi_0(\rho)|^2$ is a signature of BEC rotation. Resultsare insensitive to off-axis laser displacements $\rho_0$, for$\rho_0/\rho_{max} \ll 1$.

Macroscopic angular-momentum states of Bose-Einstein condensates in toroidal traps