  We investigate how strongly and at what scales the Sunyaev- Zel'dovich effect
reflects the shifting balance between the two processes that compete for
governing the density and the thermodynamic state of the hot intra-cluster
medium pervading clusters and groups of galaxies: the hierarchical clustering
of the DM; the non-gravitational energy and momentum fed back into the ICM by
the condensing baryons. We base on a SAM of galaxy formation and clustering to
describe how the baryons are partitioned among the hot, the cool and the
stellar phase; the partition shifts as the galaxies cluster hierarchically, and
as the feedback by stellar winds and SN explosions follows the star formation.
Their impact is amplified by the same large scale accretion shocks that
thermalize the gravitational energy of gas falling into the growing potential
wells. We compute the Compton parameter $y$, and find a relation of $y$ with
the ICM temperature, the $y-T$ relation, which departs from the self-similar
scaling and bends down at temperatures typical of galaxy groups. We
model-independently relate this with the analogous behaviour of the L_x - T
relation, and discuss to what extent our results are generic of the
hierarchical models of galaxy formation and clustering.
