A process for electrodeposition of copper on a dielectric or semiconductor base structure, the method comprising: contacting a metalizing substrate comprising a seminal conductive layer on the base structure with an aqueous electrolytic deposition composition; and supplying electrical current to the electrolytic deposition composition to deposit copper on the substrate; wherein the aqueous electrolytic composition comprises: copper ions; an acid; a suppressor; and a quaternized poly(epihalohydrin) comprising n repeating units corresponding to structure 1N and p repeating units corresponding to structure 1P: wherein Q is selected from the group consisting of: and wherein: (i) in structure IIA one of R 1, R 2 and R 3 is selected from the group consisting of unsubstituted alkyl having at least three carbon atoms, hydroxyalkyl, dihydroxyalkyl, benzyl, hydroxyphenylmethyl and dihydroxyphenylmethyl, and each of the others of R 1, R 2 and R 3 is independently selected from lower alkyl having between 1 and 3 carbon atoms; (ii) structure IIB is an N-substituted heterocyclic moiety; (iii) structure IIC is a heterocyclic moiety; and (iv) R 4 is selected from the group consisting of substituted or unsubstituted alkyl, substituted or unsubstituted alkenyl, substituted or unsubstituted alkynyl, substituted or unsubstituted aralkyl, substituted or unsubstituted alicyclic, substituted or unsubstituted aryl, and substituted or unsubstituted heterocyclic; and (v) each of R 5, R 6, R 7, R 8 and R 9 is independently selected from the group consisting of hydrogen, substituted or unsubstituted alkyl, substituted or unsubstituted alkenyl, substituted or unsubstituted alkynyl, substituted or unsubstituted aralkyl, substituted or unsubstituted alicyclic, and substituted or unsubstituted aryl, and substituted or unsubstituted heterocyclic; and wherein n is an integer between 3 and 35, p is an integer between 0 and 25; X is a halo substituent; and X- is a monovalent anion. contacting a metalizing substrate comprising a seminal conductive layer on the base structure with an aqueous electrolytic deposition composition; and supplying electrical current to the electrolytic deposition composition to deposit copper on the substrate; wherein the aqueous electrolytic composition comprises: copper ions; an acid; a suppressor; and a quaternized poly(epihalohydrin) comprising n repeating units corresponding to structure 1N and p repeating units corresponding to structure 1P: copper ions; an acid; a suppressor; and a quaternized poly(epihalohydrin) comprising n repeating units corresponding to structure 1N and p repeating units corresponding to structure 1P: wherein Q is selected from the group consisting of: and wherein: (i) in structure IIA one of R 1, R 2 and R 3 is selected from the group consisting of unsubstituted alkyl having at least three carbon atoms, hydroxyalkyl, dihydroxyalkyl, benzyl, hydroxyphenylmethyl and dihydroxyphenylmethyl, and each of the others of R 1, R 2 and R 3 is independently selected from lower alkyl having between 1 and 3 carbon atoms; (ii) structure IIB is an N-substituted heterocyclic moiety; (iii) structure IIC is a heterocyclic moiety; and (iv) R 4 is selected from the group consisting of substituted or unsubstituted alkyl, substituted or unsubstituted alkenyl, substituted or unsubstituted alkynyl, substituted or unsubstituted aralkyl, substituted or unsubstituted alicyclic, substituted or unsubstituted aryl, and substituted or unsubstituted heterocyclic; and (v) each of R 5, R 6, R 7, R 8 and R 9 is independently selected from the group consisting of hydrogen, substituted or unsubstituted alkyl, substituted or unsubstituted alkenyl, substituted or unsubstituted alkynyl, substituted or unsubstituted aralkyl, substituted or unsubstituted alicyclic, and substituted or unsubstituted aryl, and substituted or unsubstituted heterocyclic; (i) in structure IIA one of R 1, R 2 and R 3 is selected from the group consisting of unsubstituted alkyl having at least three carbon atoms, hydroxyalkyl, dihydroxyalkyl, benzyl, hydroxyphenylmethyl and dihydroxyphenylmethyl, and each of the others of R 1, R 2 and R 3 is independently selected from lower alkyl having between 1 and 3 carbon atoms; (ii) structure IIB is an N-substituted heterocyclic moiety; (iii) structure IIC is a heterocyclic moiety; and (iv) R 4 is selected from the group consisting of substituted or unsubstituted alkyl, substituted or unsubstituted alkenyl, substituted or unsubstituted alkynyl, substituted or unsubstituted aralkyl, substituted or unsubstituted alicyclic, substituted or unsubstituted aryl, and substituted or unsubstituted heterocyclic; and (v) each of R 5, R 6, R 7, R 8 and R 9 is independently selected from the group consisting of hydrogen, substituted or unsubstituted alkyl, substituted or unsubstituted alkenyl, substituted or unsubstituted alkynyl, substituted or unsubstituted aralkyl, substituted or unsubstituted alicyclic, and substituted or unsubstituted aryl, and substituted or unsubstituted heterocyclic; and wherein n is an integer between 3 and 35, p is an integer between 0 and 25; X is a halo substituent; and X- is a monovalent anion.