Original Message

An ATP certificate is required when acting as PIC under part 121. Under part 135 any scheduled operations or any aircraft acting PIC with greater than nine passengers.  Or if the company requires it.  

I say under part 135 any scheduled operations because as far as I know under HAA all operations are on demand completely different set of rules. 

12,500 pounds does not come in to play for an ATP.  

And ATP is also required under part 91K and part 91 fractional if greater than nine passengers and operating for hire. If not operating for hire you could operate a Boeing 747 with a private rating as long as you were typed and not more than nine passengers for hire.  If not for hire as many passengers as you like.