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