  We probe to what extent not only the counts of the faint blue galaxies and
their redshift distribution but also their z-resolved luminosity functions can
be explained in terms of binary merging (aggregations). We present a dynamical
theory of such interactions. On this basis we find that ``minimal
aggregations'' taking place within large scale structures and triggering
starbusts yield rates and timing such as to explain the observations of the
local, flat luminosity function and of its progressive rising and steepening
for redshifts out to $z\approx 1$. Correspondingly, we predictfaint blue counts
still rising up to $m_B\sim 28 -29$, redshift distributions shifting toward
larger z with increasing $m_B$; in addition, we predict an upturn of the faint
end of the luminosity function more pronounced in clusters than in the field.
We propose that our picture provides the differential dynamics missing in the
canonical hierarchical theories. This reconciles with the observations the
steep luminosity functions predicted at high z by such theories.
