  The locus of $\theta \equiv {k^{\mu}};_{\mu} = 0$ for bundles of light rays
emitted at noncentral points is investigated for Lema\^{\i}tre -- Tolman (L--T)
models. The three loci that coincide for a central emission point: (1) maxima
of $R$ along the rays, (2) $\theta = 0$, (3) $R = 2M$ are all different for a
noncentral emitter. If an extremum of $R$ along a nonradial ray exists, then it
must lie in the region $R > 2M$. In $2M < R \leq 3M$ it can only be a maximum;
in $R > 3M$ both minima and maxima can exist. The intersection of (1) with the
equatorial hypersurface (EHS) $\vartheta = \pi/2$ is numerically determined for
an exemplary toy model (ETM), for two typical emitter locations. The equation
of (2) is derived for a general L--T model, and its intersection with the EHS
in the ETM is numerically determined for the same two emitter locations.
Typically, $\theta$ has no zeros or two zeros along a ray, and becomes $+
\infty$ at the Big Crunch (BC). The only rays on which $\theta \to - \infty$ at
the BC are the radial ones. Along rays on the boundaries between the no-zeros
and the two-zeros regions $\theta$ has one zero, but still tends to $+ \infty$
at the BC. When the emitter is sufficiently close to the center, $\theta$ has 4
or 6 zeros along some rays (resp. 3 or 5 on the boundary rays). For noncentral
emitters in a collapsing L--T model, $R = 2M$ is still the ultimate barrier
behind which events become invisible from outside; loci (1) and (2) are not
such barriers.
