Titan Airline?
Don't know of a "Titan Airline." Titan Aviation, on the other hand, is another wholly-owned subsidy of AAWH that provides numerous services (primarily dry leasing) except crewing--AAWH will do that.
I suspect they will be the leasing agent for any AAWH tin that they cannot utilize (or can't utilized do to legal constraints, ie, GSS).
From their site: "We are focused on the acquisition, sale, dry leasing, sales leaseback, marketing and servicing of commercial aircraft and related equipment."
Don't let all the fancy Photo Shop doctoring of Atlas Air aircraft fool you.