  We face the problem to determine the slope dependent current during the
epitaxial growth process of a crystal surface. This current is proportional to
delta=(p+) + (p-), where (p+/-) are the probabilities for an atom landing on a
terrace to attach to the ascending (p+) or descending (p-) step. If the landing
probability is spatially uniform, the current is proved to be proportional to
the average (signed) distance traveled by an adatom before incorporation in the
growing surface. The phenomenon of slope selection is determined by the
vanishing of the asymmetry delta. We apply our results to the case of atoms
feeling step edge barriers and downward funnelling, or step edge barriers and
steering. In the general case, it is not correct to consider the slope
dependent current j as a sum of separate contributions due to different
mechanisms.
