The adsorption of polydisperse ideal polymer chains is shown to be sensitive to the large N tail of the distribution of chains. If and only if the number of chains decays more slowly than exponentially is there an adsorption transition like that of monodisperse infinite chains. If the number decays exponentially the adsorption density diverges continuously at a temperature which is a function of the mean chain length. At low coverages, chains with repulsive monomer-monomer interactions show the same qualitative behavior.