  We present a detailed comparison between an extended set of elemental
abundances observed in some of the most metal poor stars presently known and
the ejecta produced by a generation of primordial core collapse supernovae. We
used five stars which form our initial database and define a "template" ultra
metal poor star which is then compared to the theoretical predictions. Our main
findings are as follows: a) the fit to [Si/Mg] and [Ca/Mg] of these very metal
poor stars seems to favor the presence of a rather large C abundance at the end
of the central He burning; in a classical scenario in which the border of the
convective core is strictly determined by the Schwarzschild criterion, such a
large C abundance would imply a rather low C12(alpha,gamma)O16 reaction rate;
b) a low C abundance left by the central He burning would imply a low [Al/Mg]
(<-1.2 dex) independently on the initial mass of the exploding star while a
rather large C abundance would produce such a low [Al/Mg] only for the most
massive stellar model; c) at variance with current beliefs that it is difficult
to interpret the observed overabundance of [Co/Fe], we find that a mildly large
C abundance in the He exhausted core (well within the present range of
uncertainty) easily and naturally allows a very good fit to [Co/Fe]; d) our
yields allow a reasonable fit to 8 out of the 11 available elemental
abundances; e) within the present grid of models it is not possible to find a
good match of the remaining three elements, Ti, Cr and Ni (even for an
arbitrary choice of the mass cut); f) the adoption of other yields available in
the literature does not improve the fit; g) since no mass in our grid provides
a satisfactory fit to these three elements, even an arbitrary choice of the
initial mass function would not improve their fit.
