  We present a theoretical analysis of the competition between so-called
nuclear Jacobi and Poincar\'e shape transitions in function of spin - at high
temperatures. The latter condition implies the method of choice - a realistic
version of the nuclear Liquid Drop Model (LDM), here: the Lublin-Strasbourg
Drop (LSD) model. We address specifically the fact that the Jacobi and
Poincar\'e shape transitions are accompanied by the flattening of total nuclear
energy landscape as function of the relevant deformation parameters what
enforces large amplitude oscillation modes that need to be taken into account.
For that purpose we introduce an approximate form of the collective
Schr\"odinger equation whose solutions are used to calculate the most probable
deformations associated with both types of transitions and discuss the physical
consequences in terms of the associated critical-spin values and transitions
themselves.
