The hypothesis on the genetic connection of near-parabolic comets with Jupiter, Saturn, and the transPlutonian region (5–3000 AU) proposed by E.M. Drobyshevskii is considered. It has been shown that, on average, 5.6 comets per an area of 106 AU2 passed through the transPlutonian region during the whole history of observations. Six-hundred nineteen comets crossed the ecliptic at heliocentric distances ranging from 0 to 2 AU. As has been shown, from the total number of 945 near-parabolic comets, eight comets closely approached Jupiter and five closely approached Saturn. The Kreutz comets, 1277 objects, did not approach Jupiter closer than 3 AU. Their minimal distance to Saturn was 5.5 AU. The minimal distance of the Kreutz comets from the edge of the transPlutonian region was 28.8 AU. The analysis led to the conclusion that the concept on the origin of the near-parabolic comets suggested by Drobyshevskii is groundless.