  We consider $N_a$ three-level atoms (or systems) interacting with a one-mode
electromagnetic field in the dipolar and rotating wave approximations. The
order of the quantum phase transitions is determined explicitly for each of the
configurations $\Xi$, $\Lambda$ and $V$, with and without detuning. The
semi-classical and exact quantum calculations for both the expectation values
of the total number of excitations $\cal{M}=\langle \bm{M} \rangle$ and photon
number $n=\langle \bm{n} \rangle$ have an excellent correspondence as functions
of the control parameters. We prove that the ground state of the collective
regime obeys sub-Poissonian statistics for the ${\cal M}$ and $n$ distribution
functions. Therefore, their corresponding fluctuations are not well described
by the semiclassical approximation. We show that this can be corrected by
projecting the variational state to a definite value of ${\cal M}$.
