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An idealized model of advection and condensation of water vapor is considered as a representation of processes influencing the humidity distribution along isentropic surfaces in the free troposphere. Results are presented for how the mean relative humidity distribution varies in response to changes in the distribution of saturation specific humidity and in the amplitude of a tropical moisture source. Changes in the tropical moisture source are found to have little effect on the relative humidity poleward of the subtropical minima, suggesting a lack of poleward influence despite much greater water vapor concentrations at lower latitudes. The subtropical minima in relative humidity are found to be located just equatorward of the inflection points of the saturation specific humidity profile along the isentropic surface. The degree of mean subsaturation is found to vary with the magnitude of the meridional gradient of saturation specific humidity when other parameters are held fixed. The atmospheric relevance of these results is investigated by comparison with the positions of the relative humidity minima in reanalysis data and by examining poleward influence of relative humidity in simulations with an idealized general circulation model. It is suggested that the limited poleward influence of relative humidity may constrain the propagation of errors in simulated humidity fields. [ABSTRACT FROM AUTHOR]