  We investigate the physically accepted solutions of general Braneworld
scenarios, scanning uniformly the associated parameter space. Without making
any further assumptions we find that solutions which give "small" Hubble
parameters on the physical brane, and therefore "small" effective cosmological
constants on the 4D Universe, are far more probable than those with "large"
ones. Eventually, their distribution tends to the $\delta$-function in the
limit of continuous covering of the parameter space.
