  We present a series of arguments showing that the Seebeck coefficient can be
used as a decisive experiment to characterize the nature of the quantum
critical point (QCP) in heavy fermion compounds. Being reactive almost
exclusively to the presence of delocalized entropic carriers, the Seebeck
coefficient shows a drastic collapse at the Kondo breakdown QCP, as the
reconstruction of the Fermi surface takes place. In contrast, around a Spin
Density Wave (SDW) QCP, the Seebeck coefficient is broadly symmetric. We
discuss the possibility of a change of sign at the QCP, the characteristic
variation of $| S / T | $ with temperature and external parameter, as well as
the capacity of the Seebeck coefficient to distinguish between localized and
itinerant anti-ferromagnetism (AF). Suggestions of experiments are given in the
case of four non conventional compounds : YbRh$_2$Si$_2$, Ce(Mn)In$_5$,
CeCu$_{6-x}$Au$_x$ and URu$_2$Si$_2$.
