Absolute attachment cross sections of single molecules M (M=water, ethanol or methanol) onto positively charged mass selected clusters XnH+ (X=water, ethanol or methanol) were measured for cluster sizes ranging from tens to hundreds molecules and center-of-mass collision energies varying from 0.1 to similar to 1 eV. The attachment cross sections, which converge as expected towards geometrical cross sections at large cluster sizes, are systematically and noticeably lower than geometrical cross sections at small sizes. Attachment cross sections depend barely on the nature of the reactants. Homogeneous attachment reactions XnH+ + X -> Xn+1H+ can be accounted for by a dynamical collisional model, in which the intermolecular interactions between the target cluster and the impinging molecule can be neglected. Dynamical arguments accounts satisfactorily for size and energy dependences of attachment cross sections and also for their variation from one element to another. It is thus suggested that either the attachment probabilities are likely to be more governed by the capacity of clusters to absorb collision energy rather than by cluster/molecule intermolecular interactions, or it indicates that the strength of these interactions does not differ noticeably among the hydrogen-bonded systems investigated. However, for inhomogeneous reactions of the form XnH+ + Y -> XnYH+ (X, Y=water, ethanol, methanol), although the global size dependences are qualitatively reproduced, the variations of attachment cross sections with the nature on the impinging molecule are not satisfactorily accounted for within the simple empirical model proposed for homogeneous reactions.