  The production of all identified hadrons at the CERN Large Hadron Collider
(LHC) is studied with emphasis on the $p_T$ distributions up to 20 GeV/c in
central collisions at $\sqrt{s_{NN}}=2.76$ TeV. The parton recombination model
is used to determine the hadronic \ppt\ spectra from the quark \dis s. From the
heavy hyperon spectra it is known from earlier studies that the $u, d, s$
thermal \dis s in \ppt\ are exponential with large inverse slopes that cannot
be identified with any temperature in conventional fluid models. They are used
as inputs in our model together with shower partons determined from our
treatment of momentum degradation that uses high-\ppt\ pion data as input.
Those thermal and shower partons are used to calculate the $p_T$ \dis s of all
observed hadrons ($\pi, K, p, \Lambda$, $\Xi$, $\Omega$ and $\phi$) over wide
ranges of \ppt, so the system is highly constrained. We show how well the LHC
data can be reproduced with only a few parameters to adjust. Centrality
dependence has not been studied. What is learned is that minijets are
important, not only in giving rise to abundant shower partons, but also in the
conversion of semihard partons in the medium to soft partons that enhance the
thermal partons. Since the conversion process can occur throughout the
expansion phase of the high-density medium, this work provides the basis for
questioning the validity of the assumption of rapid equilibration.
