The biggest moose ever shot was in Alaska on September 5th 2004 by a hunter named Eric Arnette. With an astonishing weight of over 2300 pounds and 15" tall, this is a remarkable creature. You can see from the following picture how big the moose really was.
Killed using a .338 at 50 yards, it was very difficult to take the large moose down - as a matter of fact, it took 40 minutes and two guides to kill the moose. The animal had extremely large paddles. The area where this moose was captured is very remote and accessing it is very difficult.
In this region, moose have opportunity to reach maturity (and from the looks of it, this particular moose reached it). The genetics here are some of the best available around the entire world due to the fact that humans don't interfere at all.
The second largest world record bull moose ever caught was also in Alaska with a score of 255 1/2 inches B & C and measuring 76 3/4 inches. The moose was killed by a 10 year old boy named Jack Frances Nelsen, following his father instructions who told him exactly what to do and when to shoot the large animal.
They couldn't believe the dimensions of the moose, it was almost incredible. You can imagine how long it took to skin down the moose. Here is a picture with the second largest moose ever caught:
These are only two examples of some large moose specimens captured. You will have bigger chances of catching larger moose if you try to hunt in remote areas (where they can reach full maturity, without the interference of humans), where these animals aren't hunted often due to the fact that access to these areas is pretty difficult.