By a combination of analytical and numerical methods, the density prof
ile of a spherical star momentarily at rest is varied, and the corresp
onding response in the area of the spherical shells is monitored. it i
s shown that the inner apparent horizon (if it exists) must lie within
or at most on the star's surface while no such restriction is found f
or the outer apparent horizon. An apparent horizon, however, lying in
the vacuum region will always have a nonvanishing area, as long as the
ADM mass of the system is nonzero. Furthermore for density profiles n
ot decreasing outwards, it appears that all spherical trapped surfaces
lie on a thick spherical shell. Finally for a uniform density star a
simple criterion is found, relating the density and proper radius that
guarantees the presence or absence of trapped regions.