  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 k$_t$-factorization approaches in the past. We show that the present
knowledge of gluon distributions does not allow to make a precise predictions
for $c \bar c$ production at LHC, in particular at forward rapidities. In this
paper we study production of $c \bar c$ pairs including several subleading
mechanisms. This includes: $gg \to Q \bar Q$, $\gamma g \to Q \bar Q$, $g
\gamma \to Q \bar Q$, $\gamma \gamma \to Q \bar Q$. 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 ($\bar c$ antiquark)
rapidity and transverse momenta and compare them to the dominant gluon-gluon
fusion contribution. 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. Finally 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.
