Branched polymers are prepared from at least (A) at least one monomer having an electron donor moiety, (B) at least one monomer having an electron acceptor moiety, and (C) at least one multifunctional branching agent comprising a urea moiety and at least two N-vinyl groups. The branched polymers are least 20% (by weight) soluble in a solvent for which the corresponding polymer of equal molecular weight made without said multifunctional branching agent is at least 20% (by weight) soluble. Due in part to the wide range of chemistries and solubility and rheological properties, the branched polymers find application in personal care, pharmaceutical/nutritional, and performance chemicals compositions.