  At high-energies the gluon-gluon fusion is the dominant mechanism of c \bar c
production. This process was calculated in the NLO collinear as well as in the
kt-factorization approaches in the past. In this presentation we concentrate on
production of c \bar c pairs including several subleading mechanisms. In this
context we use MRST-QED parton distributions which include photon as a parton
in the proton as well as elastic photon distributions calculated in the
equivalent photon approximation. We present distributions in the c quark (c
antiquark) rapidity and transverse momenta and compare them to the dominant
gluon-gluon fusion contribution.valent photon approximation. We discuss also
inclusive single and central diffractive processes using diffractive parton
distribution found from the analysis of HERA diffractive data. As in the
previous case we present distribution in c \bar c rapidity and transverse
momentum. Next we present results for exclusive central diffractive mechanism
discussed recently in the literature. We show corresponding differential
distributions and compare them with corresponding distributions for single and
central diffractive components. Finally we discuss production of two pairs of c
\bar c within a simple formalism of double-parton scattering (DPS).
Surprisingly very large cross sections, comparable to single-parton scattering
(SPS) contribution, are predicted for LHC energies.
