  We study z-automorphisms of the polynomial algebra K[x,y,z] and the free
associative algebra K<x,y,z> over a field K, i.e., automorphisms which fix the
variable z. We survey some recent results on such automorphisms and on the
corresponding coordinates. For K<x,y,z> we include also results about the
structure of the z-tame automorphisms and algorithms which recognize z-tame
automorphisms and z-tame coordinates.
