Is there any relationship between the height of a tree and the number of branches emerging from the main stem? Is there any relationship between the height of a tree and the number of branches emerging from the main stem? I am particular interested in spruce or fir.

The height is only one of a few factors; also the species and environment are more significant. A spruce growing in unshaded location may have branches to ground level while the same species in a dense woods will only have branches at the top. A southern pine ( in the US) is often 100 ft tall with all the branches in the top 30 ft ; these trees drop the lower branches because of limited light and because various vines climb into the lower branches ( until the branches die and fall).