  A well known Conjecture due to Beloshapka asserts that all totally
nondegenerate polynomial models with the length $l\geq 3$ of their Levi-Tanaka
algebra are {\em rigid}, that is, any point preserving automorphism of them is
completely determined by the restriction of its differential at the fixed point
onto the complex tangent space. For the length $l=3$, Beloshapka's Conjecture
was proved by Gammel and Kossovskiy in 2006. In this paper, we prove the
Conjecture for arbitrary length $l\geq 3$.
  As another application of our method, we construct polynomial models of
length $l\geq 3$, which are not totally nondegenerate and admit large groups of
point preserving nonlinear automorphisms.
