It is likely that many airlines accommodate people who are being deported as regular passengers on outbound international flights.

For movement of humans at industrial scale, though, there are only a few operators with ICE contracts. Avelo, GlobalX, Eastern, Key Lime Air, and Omni come immediately to mind. For international flights, there's at least one Learjet operator that flies a bunch for them, too.

These days, the aforementioned carriers fly 20-30 flights/day. Here are Saturday's flights (apologies for the sign-in wall, but lalabote keeps their account somewhat locked down): https://bsky.app/profile/lalabote.bsky.social/post/3mai6lach...

I think Avelo is the only airline that participates. The rest are charter companies.

Key Lime Air operates daily airline flights as Denver Air Connection in addition to their charter work for ICE and others.