Morgan. All over. I don't see quarter horse- every inch of him screams morgan to me... As for your doubts due to his thicker build than 'arabian-like morgans', look up 'Lippitt morgan horse'- Lippitts are bred to the standards of the original morgan horse, and those guys are THICK, lol.
There are different types of morgans, just like there are different types of arabians and quarter horses. And to add to that, individual horses can look even MORE like a different breed. Does he have papers? Try researching his bloodlines, so you can see what's in his bloodlines, and maybe contact his breeder. :)