  We consider the XXX homogeneous Gaudin system with $N$ sites, both in
classical and the quantum case. In particular we show that a suitable limiting
procedure for letting the poles of its Lax matrix collide can be used to define
new families of Liouville integrals (in the classical case) and new "Gaudin"
algebras (in the quantum case). We will especially treat the case of total
collisions, that gives rise to (a generalization of) the so called Bending
flows of Kapovich and Millson. Some aspects of multi-Poisson geometry will be
addressed (in the classical case). We will make use of properties of "Manin
matrices" to provide explicit generators of the Gaudin Algebras in the quantum
case.
