We exhibit and discuss the QCD prediction for the transverse momentum distribution of W bosons, Z bosons and high-mass virtual photons produced in high-energy hadron-hadron collisions. Recent work has shown that this prediction is consistent with the structure of leading twist initial state interactions. The expression we present is expected to give results correct up to order αsN(Q) for anyQT when the boson mass Q is very large (> 108 GeV!), given only input from perturbative calculations at order αsN+2 and deeply inelastic scattering structure functions. We specify the required N = 0 coefficients, employing the order αs2 results of Kodaira and Trentadue and of Davies and Stirling. We then show how the expression should be modified to deal with current energy scales. We also discuss the connection between low-QT and high-QT formulae.