Formation of highly-branched off-stoichiometric polymers from A(x) + B-y monomers has been described theoretically using a statistical branching theory in which the irreversibility of bond formation was respected. The critical molar ratio (CMR) of A to B groups, i.e., such excess of groups of one type beyond which the system does not gel and only soluble highly-branched polymers are formed, was calculated. CMR depends on the functionality of the components and on the reactivity of functional groups involved in formation of bonds. For an increasing excess of A groups over B groups, soluble A-functional polymers of decreasing molecular weight are formed. When monofunctional monomer is added, the number-average molecular weights and degrees of polymerization as well as the number of functional groups per molecule remain relatively low even at the CMR when the gel point is reached. When one A group in the A3 monomer has higher reactivity than the remaining two and also in B2 where the reactivities of B groups are different, the value of CMR decreases from 2 towards 1.5, which is the limiting case. Important is that with increasing differences in reactivity the range of molecular weights can be extended and the polydispersity can be suppressed. Functional highly-branched polymers of reasonable molecular weight and polydispersity can be obtained, which in their application can compete with conventional hyperbranched polymers. The use of the information obtained in this description of crosslinking of the highly-branched off-stoichiometric polymers is outlined. (c) 2005 Elsevier Ltd. All rights reserved.