  The existence of dual structures in a Yangian Y(g) signify that the latter
belongs to multidimensional naturally parametrized variety of Hopf algebras.
These varieties have boundaries containing Yangians Y(a) inequivalent to the
original Y(g). The new basic algebra $a$ is an algebra of the cotangent bundle
attributed to the dual structure. We show how to construct such boundary
Yangians and study some of their properties. We prove that the Hopf algebra
Y(a) is a quantization of a parametric solution of the classical Yang-Baxter
equation. The limiting procedure and the properties of the boundary Yangians
are demonstrated explicitly for the case of Y(sl(2)).
