In radiofrequency (RF) helicon discharges the electromagnetic power is transferred from the RF field irradiated by the antenna to the plasma medium by means of plasma-wave coupling of the electromagnetic wave with the electrons. For the common industrial frequencies of tens of MHz, and for typical pressures of few Pascals, the power deposition occurs mostly at the edge of the discharge. In these conditions, ionization and electron heating occur in a layer close to the chamber walls, where a consistent fraction of the plasma is rapidly lost by diffusion toward the surface. The remaining fraction of plasma diffuses inward toward the center of the discharge, setting up a uniform and almost flat density profile, used in applications. A one-dimensional model considering both the plasma-wave coupling of the electrons with the RF wave and the macroscopic transport of ions and neutrals along the radial dimension of a cylindrical processing chamber has been derived and used to evaluate the profiles at equilibrium. The model has been validated through Langmuir probe measurements in helicon processing chambers. The numerical model has then been used to study the power-coupling behavior of the discharge when the pressure of the neutral gas is decreased. When the Knudsen number of the neutral gas approaches unity and in conditions of slightly magnetized discharge, the power deposition shifts from being edge-localized to center-localized, thus reducing the particle fluxes toward the walls and increasing the efficiency of the coupling.