  We study automorphisms of the free associative algebra K<x,y,z> over a field
K which fix z and such that the images of x, y are linear with respect to x, y.
We prove that some of these automorphisms are wild in the class of all
automorphisms fixing z, including the well known automorphism discovered by
Anick, and show how to recognize the wild ones. This class of automorphisms
induces tame automorphisms of the polynomial algebra K[x,y,z]. For n>2 the
automorphisms of K<x_1,...,x_n,z> which fix z and are linear in the x's are
tame.
