  This paper considers the dynamics of scattering of planetesimals or planetary
embryos by a planet on a circumstellar orbit. We classify six regions in the
planet's mass versus semimajor axis parameter space according to the dominant
outcome for scattered objects: ejected, accreted, remaining, escaping, Oort
Cloud, depleted Oort Cloud. We use these outcomes to consider which planetary
system architectures maximise the observability of specific signatures, given
that signatures should be detected first around systems with optimal
architectures (if such systems exist in nature). Giant impact debris is most
readily detectable for 0.1-10Mearth planets at 1-5au, depending on detection
method and spectral type. While A stars have putative giant impact debris at
4-6au consistent with this sweet spot, that of FGK stars is typically <<1au
contrary to expectations; an absence of 1-3au giant impact debris could
indicate a low frequency of terrestrial planets there. Three principles
maximise cometary influx from exo-Kuiper belts: a chain of closely separated
planets interior to the belt, none of which is a Jupiter-like ejector; planet
masses not increasing strongly with distance (for a net inward torque on
comets); ongoing replenishment of comets, possibly by embedded low-mass
planets. A high Oort Cloud comet influx requires no ejector and architectures
that maximise the Oort Cloud population. Cold debris disks are usually
considered classical Kuiper belt analogues. Here we consider the possibility of
detecting scattered disk analogues, which could be betrayed by a broad radial
profile and lack of small grains, as well as spherical 100-1000au mini-Oort
Clouds. Some implications for escaping planets around young stars, detached
planets akin to Sedna, and the formation of super-Earths, are also discussed.
