  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 the merger point
geometry does not approach a black hole away from the neck. We cannot rule out
a topology changing phase transition as argued by Kol. However as the merger
point geometry does not approach the black hole geometry asymptotically it is
not obvious that the transition is directly to a black hole phase. We also
demonstrate that for another range of the Gauss-Bonnet parameter, the merger
point geometry approaches the black hole geometry asymptotically when a certain
parameter depending on the Gauss-Bonnet parameter $\alpha$ and on the
parameters in the Einstein-Gauss-Bonnet black hole metric is small enough.
