  The creation of particles with large transverse momenta in high energy
hadronic collisions is a long standing problem. The transition from small-
(soft) to hard- parton scattering `high-pt' events is rather smooth. In this
paper we apply the non-extensive statistical framework to calculate transverse
momentum distributions of long lived hadrons created at energies from low
(sqrt(s)~10 GeV) to the highest energies available in collider experiments
(sqrt(s)~2000 GeV). Satisfactory agreement with the experimental data is
achieved. The systematic increase of the non-extensivity parameter with energy
found can be understood as phenomenological evidence for the increased role of
long range correlations in the hadronization process.
  Predictions concerning the rise of average transverse momenta up to the
highest cosmic ray energies are also given and discussed.
