The most dramatic display of variable activity of a comet is splitting of the nucleus. For the purpose of revealing the trends of splitting of comet nuclei and of formation of abnormal cometary tails, we have created two catalogues of comets: a catalogue of split nuclei, containing 99 comets, and a catalogue of comets with abnormal tails, including 60 objects. Statistical investigation reveals some general trends of these phenomena. The greatest number of recorded cases of nucleus splitting and abnormal tail (60%) occurs within an interval of heliocentric distance ranging from 0.6 AU to 1.6 AU (maximum at 1.1 AU) and geocentric distance ranging from 0.6 AU to 1.8 AU (maximum at 1.15 AU). Splitting of nuclei and abnormal tails are more often (75%) recorded close to the perihelia of the cometary orbits. Only 16% of splitting comets also exhibit abnormal tails. Some cases of nuclear splitting and large velocity (some km/s) eruptions of dust from a nucleus, as well as cases of abnormal tails developed at large heliocentric distances, may indicate collisions of comet nuclei with other bodies. Our results are of interest for the physics of comets, and for the distribution of meteoroids in solar system.