Most planetesimals formed at distances of 15 - 30 a.u. were gravitationally ejected from the Solar system as a result of the migration of the giant planets, but a small part remained, captured by Jupiter and the Kuiper belt. As a result, we can now observe such a variety, in terms of physical and dynamic characteristics, in the Trojan asteroids of Jupiter and in the Kuiper belt. Planetesimals captured by the Kuiper Belt are a "hot population" now. The term "hot" does not refer to the temperature of bodies, but characterizes the orbit of objects. ~120,000 objects larger than 100 km. in diameter are known in the "hot population". This population is characterized by an orbital inclina- tion greater than 5 degrees and a large eccentricity. The main task of the work, based on physical and dynamic characteristics, is to search for the same properties Trojan asteroids of Jupiter and objects from the "hot population" of the Kuiper belt, which supposedly migrated earlier from the region of the original orbit of Neptune. The data from ground-based observations and space missions is used in the work.