Thermoplastic molding compositions, comprising A) from 10 to 98% by weight of at least one thermoplastic polymer, B) from 0.01 to 50% by weight of B1) at least one highly branched or hyperbranched polycarbonate having an OH number of from 1 to 600 mg KOH/g of polycarbonate (to DIN 53240, Part 2), or B2) at least one highly branched or hyperbranched polyester of AxBy type, where x is at least 1.1 and y is at least 2.1, or a mixture of these, C) from 1 to 40% by weight of a halogen-free flame retardant, selected from the group of the phosphorus-containing or nitrogen-containing compounds, or of the P—N condensates, or a mixture of these, D) from 0 to 60% by weight of other additives, where the total of the percentages by weight of components A) to D) is 100%.