About hybrid/overlay

Dear Lammps Developers,
Is pair hybrid/overlay adding two functions directly, or is it the final potential function where each contributes 50% of the force and potential?
This issue does not seem to be explained in detail on the official website.
Thank you

From the LAMMPS ManualTM:

For the hybrid/overlay and hybrid/scaled styles, each atom type pair I,J can be assigned to one or more sub-styles. If you specify the same atom type pair in a second pair_coeff command with a new sub-style, then the second sub-style is added to the list of potentials that will be calculated for two interacting atoms of those types.

Regarding your question:

This depends on how you specify the pair_coeff.

pair_style hybrid/overlay lj/cut 12.0 buck 8.5
pair_coeff 1*2 1*2 lj/cut 6. 1.8
pair_coeff 3 3 buck 100.0 1.5 200.0
pair_coeff 1 3 lj/cut 4. 2.5

In this case, on atom type 1 you would have force contributions from the two pair styles (and from atom types 1,2,3), on atom 2 you would have force contributions coming only from pair_style lj/cut (and from atom types 1,2), while for atom type 3 you would have force contributions from the two pair styles (but only from atom types 1 and 3).