  (*** abridged ***) Context: The wings of Balmer lines are often used as
effective temperature diagnostics for late-type stars under the assumption they
form in local thermodynamic equilibrium.
  Aims: Our goal is to investigate the non-LTE formation of Balmer lines in
late-type stellar atmospheres, to establish if the assumption of LTE is
justified. Furthermore, we aim to determine which collision processes are
important for the problem; in particular, the role of collision processes with
hydrogen atoms is investigated.
  Method: A model hydrogen atom for non-LTE calculations has been constructed
accounting for various collision processes using the best available data from
the literature. The processes included are inelastic collisions with electrons
and hydrogen atoms, mutual neutralisation and Penning ionisation. Non-LTE
calculations are performed, and the relative importance of the collision
processes is investigated.
  Results: Our calculations show electron collisions alone are not sufficient
to establish LTE for the formation of Balmer line wings. The role of inelastic
collisions with neutral hydrogen is unclear. The available data for these
processes is of questionable quality, and different prescriptions for the rate
coefficents give significantly different results for the Balmer line wings.
  Conclusions: Improved calculations or experimental data are needed for
excitation and, particularly, ionisation of hydrogen atoms in low-lying states
by hydrogen atom impact at near threshold energies. Until such data are
available, the assumption of LTE for the formation of Balmer line wings in
late-type stars is questionable.
