  There is an intrinsic notion of what it means for a contact manifold to be
the smooth boundary of a Stein manifold. The same concept has another more
extrinsic formulation, which is often used as a convenient working hypothesis.
We give a simple proof that the two are equivalent. Moreover it is shown that,
even though a border always exists, it's germ is not unique; nevertheless the
germ of the Dolbeault cohomology of any border is unique. We also point out
that any Stein fillable compact contact 3- manifold has a geometric realization
in C^4 via an embedding, or in C^3 via an immersion.
