  We derive the probability that a randomly chosen NL-node over $S$ gets
localized as a function of a variety of parameters. Then, we derive the
probability that the whole network of NL-nodes over $S$ gets localized. In
connection with the asymptotic thresholds, we show the presence of asymptotic
thresholds on the network localization probability in two different scenarios.
The first refers to dense networks, which arise when the domain $S$ is bounded
and the densities of the two kinds of nodes tend to grow unboundedly. The
second kind of thresholds manifest themselves when the considered domain
increases but the number of nodes grow in such a way that the L-node density
remains constant throughout the investigated domain. In this scenario, what
matters is the minimum value of the maximum transmission range averaged over
the fading process, denoted as $d_{max}$, above which the network of NL-nodes
almost surely gets asymptotically localized.
