  We consider properties of near-critical solutions describing a test static
axisymmetric D-dimensional brane interacting with a bulk N-dimensional black
hole (N>D). We focus our attention on the effects connected with curvature
corrections to the brane action. Namely, we demonstrate that the second order
phase transition in such a system is modified and becomes first order. We
discuss possible consequences of these results for merger transitions between
caged black holes and black strings.
