  A thick Z_2-symmetric domain wall supported by a scalar field with an
arbitrary potential V(\phi) in 5D general relativity is considered as a
candidate brane world. We show that, under the global regularity requirement,
such a configuration (i) has always an AdS asymptotic far from the brane, (ii)
is only possible if V(\phi) has an alternating sign and (iii) V(\phi) satisfies
a certain fine-tuning type equality. The thin brane limit is well defined and
conforms to the Randall-Sundrum (RS2) brane world model if the asymptotic value
of V(\phi) (related to \Lambda, the effective cosmological constant) is kept
thickness-independent. Universality of such a transition is demonstrated using
as an example exact solutions for stepwise potentials of different shapes.
Also, due to scale invariance of the Einstein-scalar equations, any given
regular solution creates a one-parameter family of solutions with different
potentials. In such families, a thin brane limit does not exist while the ratio
\Lambda/(brane tension)^2 is thickness-independent and is in general different
from its value in the RS2 model.
