  We investigate the behaviour of cosmological baryons at low redshifts $z<5$
after reionization through analytic means. In particular, we study the
density-temperature phase-diagram which describes the history of the gas. We
show how the location of the matter in this $(\rho,T)$ diagram expresses the
various constraints implied by usual hierarchical scenarios. This yields robust
model-independent results which agree with numerical simulations. The IGM is
seen to be formed via two phases: a ``cool'' photo-ionized component and a
``warm'' component governed by shock-heating. We also briefly describe how the
remainder of the matter is distributed over galaxies, groups and clusters. We
recover the fraction of matter and the spatial clustering computed by numerical
simulations. We also check that the soft X-ray background due to the ``warm''
IGM component is consistent with observations. We find in the present universe
a baryon fraction of 7% in hot gas, 24% in the warm IGM, 38% in the cool IGM,
9% within star-like objects and, as a still un-observed component, 22% of dark
baryons associated with collapsed structures, with a relative uncertainty no
larger than 30% on these numbers.
