Let
K
K
be a field of characteristic zero. We characterize coordinates and tame coordinates in
K
[
z
]
[
x
,
y
]
K[z][x,y]
, i.e. the images of
x
x
respectively under all automorphisms and under the tame automorphisms of
K
[
z
]
[
x
,
y
]
K[z][x,y]
. We also construct a new large class of wild automorphisms of
K
[
z
]
[
x
,
y
]
K[z][x,y]
which maps
x
x
to a concrete family of nice looking polynomials. We show that a subclass of this class is stably tame, i.e. becomes tame when we extend its automorphisms to automorphisms of
K
[
z
]
[
x
,
y
,
t
]
K[z][x,y,t]
.