  We investigate numerically the role of thermal instability (TI) as a
generator of density structures in the interstellar medium (ISM), both by
itself and in the context of a globally turbulent medium. Simulations of the
instability alone show that the condenstion process which forms a dense phase
(``clouds'') is highly dynamical, and that the boundaries of the clouds are
accretion shocks, rather than static density discontinuities. The density
histograms (PDFs) of these runs exhibit either bimodal shapes or a single peak
at low densities plus a slope change at high densities. Final static situations
may be established, but the equilibrium is very fragile: small density
fluctuations in the warm phase require large variations in the density of the
cold phase, probably inducing shocks into the clouds. This result suggests that
such configurations are highly unlikely. Simulations including turbulent
forcing show that large- scale forcing is incapable of erasing the signature of
the TI in the density PDFs, but small-scale, stellar-like forcing causes
erasure of the signature of the instability. However, these simulations do not
reach stationary regimes, TI driving an ever-increasing star formation rate.
Simulations including magnetic fields, self-gravity and the Coriolis force show
no significant difference between the PDFs of stable and unstable cases, and
reach stationary regimes, suggesting that the combination of the stellar
forcing and the extra effective pressure provided by the magnetic field and the
Coriolis force overwhelm TI as a density-structure generator in the ISM. We
emphasize that a multi-modal temperature PDF is not necessarily an indication
of a multi-phase medium, which must contain clearly distinct thermal
equilibrium phases.
