The possible functions of ceratopsian horns and frills have been debated, including fighting off predators, species recognition, and temperature control, though the dominant hypothesis involves enhancing reproductive success.
In a 2010 press release presenting Kosmoceratops, Utahceratops, and Vagaceratops, Sampson stated that most of these "bizarre features" would have been insufficient weapons against predators, but would have been used to intimidate or fight rivals of the same sex and attract individuals of the opposite sex.
In 2011, paleontologists Kevin Padian and John R. Horner proposed that "bizarre structures" in dinosaurs (including horns, frills, domes, and crests) were primarily used for species recognition (to differentiate between sympatric species; related species that lived in the same area at the same time), and they dismissed other explanations as unsupported by evidence.
They noted that many large ceratopsians had openings in their frills, making them of little use in defense, and that the wide variety in the size and orientation of their horns did not have an obvious function in combat.
They also pointed out that there is little evidence for sexual dimorphism in ceratopsians.
Responding to Padian and Horner the same year, paleontologist Rob J. Knell and Sampson argued that while species recognition could have been a secondary function of "bizarre structures", sexual selection (used in display or combat to compete for mates) was a more likely explanation because of the high cost of developing them and how they appeared to be highly variable within species.
They also pointed out that a lack of sexual dimorphism does not preclude the use of horns in mate competition; male bovines use their horns for this purpose while females use them primarily for defense and secondarily for sexual selection.

In 2013, paleontologists David E. Hone and Darren Naish criticized the "species recognition hypothesis", arguing that no extant animals use such structures primarily for species recognition and that Padian and Horner had ignored the possibility of mutual sexual selection (where both sexes are ornamented).
They noted that if the primary purpose of the structures was species recognition, they would have differed in the shape of a single structure because additional structures would have been redundant at additional cost.
Ceratopsians, for example, had elaborate nasal horn, brow horn, jugal boss, frill midline, and frill edge features, as well as differences in body size and proportions, while the absence or presence of a single horn would have been enough to differentiate between sympatric species.
In 2018, paleontologist Andrew Knapp and colleagues examined whether the diverging ornamental traits of ceratopsians were correlated with sympatricity between two or more species, as would be predicted by the "species recognition hypothesis".
They found that display patterns diverged widely overall while those of sympatric species did not differ significantly from those of non-sympatric species, concluding that the hypothesis did not have statistical support among ceratopsians.

In 2015, biologist Pasquale Raia and colleagues examined the evolutionary increase in the complexity and size of animal ornaments (such as crests, horns, and tusks) over time, using ammonites, deer, and ceratopsians as examples.
Frill complexity in ceratopsians appeared to have increased in more recent species, and Kosmoceratops had the highest values of fractal dimensions in its neck frill margin (followed by Styracosaurus, Diabloceratops, and Centrosaurus).
The authors found that ornament complexity increased with body size, suggesting that the evolution of ornament complexity was a byproduct of Cope's rule (which postulates that population lineages tend to increase in body size over evolutionary time).
They argued that though the size of most ornaments may be controlled by sexual selection (and whether they are used for choosing mates, competition, or both), it does not influence complexity and shape, concluding that it is probably the size rather
The possible functions of ceratopsian horns and frills have been debated, including fighting off predators, species recognition, and temperature control, though the dominant hypothesis involves enhancing reproductive success. In a 2010 press release presenting Kosmoceratops, Utahceratops, and Vagaceratops, Sampson stated that most of these "bizarre features" would have been insufficient weapons against predators, but would have been used to intimidate or fight rivals of the same sex and attract individuals of the opposite sex. In 2011, paleontologists Kevin Padian and John R. Horner proposed that "bizarre structures" in dinosaurs (including horns, frills, domes, and crests) were primarily used for species recognition (to differentiate between sympatric species; related species that lived in the same area at the same time), and they dismissed other explanations as unsupported by evidence. They noted that many large ceratopsians had openings in their frills, making them of little use in defense, and that the wide variety in the size and orientation of their horns did not have an obvious function in combat. They also pointed out that there is little evidence for sexual dimorphism in ceratopsians. Responding to Padian and Horner the same year, paleontologist Rob J. Knell and Sampson argued that while species recognition could have been a secondary function of "bizarre structures", sexual selection (used in display or combat to compete for mates) was a more likely explanation because of the high cost of developing them and how they appeared to be highly variable within species. They also pointed out that a lack of sexual dimorphism does not preclude the use of horns in mate competition; male bovines use their horns for this purpose while females use them primarily for defense and secondarily for sexual selection.
In 2013, paleontologists David E. Hone and Darren Naish criticized the "species recognition hypothesis", arguing that no extant animals use such structures primarily for species recognition and that Padian and Horner had ignored the possibility of mutual sexual selection (where both sexes are ornamented). They noted that if the primary purpose of the structures was species recognition, they would have differed in the shape of a single structure because additional structures would have been redundant at additional cost. Ceratopsians, for example, had elaborate nasal horn, brow horn, jugal boss, frill midline, and frill edge features, as well as differences in body size and proportions, while the absence or presence of a single horn would have been enough to differentiate between sympatric species. In 2018, paleontologist Andrew Knapp and colleagues examined whether the diverging ornamental traits of ceratopsians were correlated with sympatricity between two or more species, as would be predicted by the "species recognition hypothesis". They found that display patterns diverged widely overall while those of sympatric species did not differ significantly from those of non-sympatric species, concluding that the hypothesis did not have statistical support among ceratopsians.
In 2015, biologist Pasquale Raia and colleagues examined the evolutionary increase in the complexity and size of animal ornaments (such as crests, horns, and tusks) over time, using ammonites, deer, and ceratopsians as examples. Frill complexity in ceratopsians appeared to have increased in more recent species, and Kosmoceratops had the highest values of fractal dimensions in its neck frill margin (followed by Styracosaurus, Diabloceratops, and Centrosaurus). The authors found that ornament complexity increased with body size, suggesting that the evolution of ornament complexity was a byproduct of Cope's rule (which postulates that population lineages tend to increase in body size over evolutionary time). They argued that though the size of most ornaments may be controlled by sexual selection (and whether they are used for choosing mates, competition, or both), it does not influence complexity and shape, concluding that it is probably the size rather 
Kosmoceratops