You guys got me interested. Does anyone know the heritabilty rate of antler expression?

THe offspring will carry half of the doe's genetic material and half of the buck's gene(s) that mated with the doe.

I may be wrong, but I doubt if there is only one gene that influences antler expression. This means that simple dominant and recessive factor would not apply.

If my assumption is true, that means you may only increase or decrease antler expression by so much of a percent in any one generation. And of course there would a lot of variabilty among offsprings even if they had the same parents.

Then, there is the environmental effect on the expression of the trait. So, even if the buck had world class genetics for antler growth, and is unfortunate enough to live in a time or place of some limiting environmental factors (drought, soils low in minerals, etc.), he may never obtain the antlers that he could potentially have.

I could rattle on.

The answer to your question is that the average of the offsprings of the doe fawns sire by the huge buck should have antlers between the mediocre buck and the huge buck. There will be a lot of variability in the offspring due to the toss of the dice in gene combination and the environment in which the offsprings are born in.