  We study the formation of marginally trapped surfaces in the head-on
collision of two ultrarelativistic charges in $(A)dS$ space-time. The metric of
ultrarelativistic charged particles in $(A)dS$ is obtained by boosting
Reissner-Nordstr\"om $(A)dS$ space-time to the speed of light. We show that
formation of trapped surfaces on the past light cone is only possible when
charge is below certain critical - situation similar to the collision of two
ultrarelativistic charges in Minkowski space-time. This critical value depends
on the energy of colliding particles and the value of a cosmological constant.
There is richer structure of critical domains in $dS$ case. In this case
already for chargeless particles there is a critical value of the cosmological
constant only below which trapped surfaces formation is possible. Appearance of
arbitrary small nonzero charge significantly changes the physical picture.
Critical effect which has been observed in the neutral case does not take place
more. If the value of the charge is not very large solution to the equation on
trapped surface exists for any values of cosmological radius and energy density
of shock waves. Increasing of the charge leads to decrease of the trapped
surface area, and at some critical point the formation of trapped surfaces of
the type mentioned above becomes impossible.
