Capt
It is down to the handling agent to supply the tug plus any other equipment for example engineer/coaches etc but if we did ring round then 99 times out of a hundred the answer would be
" we dont handle SAA we have our own aircraft to handle" and we would have no joy. That time of the morning is normally a problem anyway.
Regarding BA we have our own problems with them regarding response times and have even comandered tugs on the taxiway to attend a disable aircraft.
I think Gonzo would bear me out on this one !!!