  We investigate the presence of a black hole black string phase transition in
Einstein Gauss Bonnet (EGB) gravity in the large dimension limit. The merger
point is the static spacetime connecting the black string phase with the black
hole phase. We consider several ranges of the Gauss-Bonnet parameter. We find
that there is a range when the Gauss-Bonnet corrections are subordinate to the
Einstein gravity terms in the large dimension limit, and yet there is no merger
point geometry possible. It is possible to have a merger point provided the
Gauss-Bonnet parameter $\alpha$ is such that a certain parameter depending on
$\alpha$, and on the parameters in the Einstein-Gauss-Bonnet black hole metric
is small enough. Finally we speculate on whether the existence of the merger
point depends on the size of the extra dimension in EGB gravity and also
whether the property of copying of solutions that is seen in Einstein gravity
occurs in EGB gravity.
