  The characterization of small samples of cold bosonic atoms in rotating
microtraps has recently attracted increasing interest due to the possibility to
deal with a few number of particles per site in optical lattices. We analyze
the evolution of ground state structures as the rotational frequency $\Omega$
increases. Various kinds of ordered structures are observed. For $N<10$ atoms,
the standard scenario, valid for large sytems, is absent, and only gradually
recovered as $N$ increases. The vortex contribution to the total angular
momentum $L$ as a function of $\Omega$ ceases to be an increasing function of
$\Omega$, as observed in experiments of Chevy {\it et al.} (Phys. Rev. Lett.
85, 2223 (2000)). Instead, for small $N$, it exhibits a sequence of peaks
showing wide minima at the values of $\Omega$, where no vortices appear.
