What is the maximum range on a 50 BMG without any hold over?

How big is the target, what is your zero?

The trajectory is ~ on par with most hunting rifles, which would be 250-300 yds for center of mass hit.

There is a HUGE misconception about the .50 BMG. It is not the laser beam that a lot of people think it is, nor does it make hitting a target at long range any easier. For example, my .50 BMG, shooting a 750 gr. A-Max, sighted in with a 500 yard zero, is 18 inches high at 300 yards, and down 188" at 1000 yards. Now, I would not call that particularly flat shooting, would you? What it does do is hold its velocity better than smaller rounds with lighter bullets, therefore staying supersonic and holding it accuracy longer. It is still affected by wind, which in a 10 mph wind will be blown almost 10 inches at 500 yards, and it still under the influence of gravity.

on a elk or bear sized animal, what is the maximum range a shot could be fired without rising more than 3" above the line of sight,

I dont want a laser beam. I dont want a 500yd shooter. I want 750 grains at 12,000 foot-pounds and 2,600 feet per second.

With my scope height being 3.5" above the bore, the minimum kill zone I can put in my computer is 7", so for a MPBR using 3.5" +- the MPBR is 304 yds with a zero at 260. If you put your scope at 3" above bore (giving you a 6" kill zone), then the MPBR drops to 285 yards with a zero at 246.