Aqueous paper coating compositions containing at least one of a clay, a starch, casein, a resin, and a wax; and wherein the composition contains from about 0.001% to about 5% by weight of at least one base-catalyzed branched reaction product comprising the following reactants: A) at least one compound of formula I R1(X)3  (I)  wherein each X group is a halogen atom or one X group is a halogen atom and two X groups represent an epoxy oxygen atom, which is attached to two adjacent carbon atoms in the R1 group to form an epoxy group, and R1 is an alkanetriyl group containing from 3 to 10 carbon atoms; and B) at least one compound having the formula II R2X(AO)nY  (II)  wherein R2 is a substituted or unsubstituted, saturated or unsaturated, organic group having from 1 to 36 carbon atoms; X is —O—, —S—, or —NR3— where R3 is hydrogen or a C1-C18 alkyl group; each AO group is independently an ethyleneoxy, 1,2-propyleneoxy, or 1,2-butyleneoxy group, n is a number from 0 to 200; and Y is hydrogen, or Y can be a mercapto group or an amino group (amino or C1-C6 alkylamino group) in place of a terminal —OH group, provided that when Y is mercapto or an amino group, n is at least 1; wherein the mole ratio of the linking compound A) to B) is from 0.1:1 to 5:1.