I think that a lot of people here are making a lot of assumptions.

I expect that the LAN takeover of JJ will go ahead, but that in itself is no guarantee that JJ will end up in OW.

I would think that the Brazilian authorities would look long and hard at whether the combo of AA/ LATAM/ IAG is something they would be happy with.

It is entirely possible that they will say "yes" to the takeover, and "no" to a JJ move to OW due to the concentration of market share they may be forced to stay in two separate alliances post merger if they cannot get regulatory approval for JJ to move to OW (All it would take is for the Brazilian authorities to say that they would not approve JJ resuming a frequent flyer earning and redemption agreement with AA - since ff reciprocity is a pre-requisite of membership - and that would mean that JJ could not move) The US-Brazil market has changed considerably since the last time that AA and JJ had a frequent flyer agreement - RG has disappeared and JJ flies a much more substantial USA schedule, so it is by no means a foregone conclusion that authorities would permit a tie-up between JJ and AA to be resumed.