Continuous process for preparation of polyalkylene arylates A) comprising highly branched or hyperbranched polymers B) and, if appropriate, comprising lubricants C), by esterifying or transesterifying an aromatic dicarboxylic acid or its ester or ester-forming derivatives, with a molar excess of an aliphatic dihydroxy compound, and polycondensing the resultant transesterification or esterification product, which comprises, on achievement of at least 80% of the desired viscosity number, adding component B) and also, if appropriate, C) to the polymer melt, and, if appropriate, post-condensing the melt and then discharging, cooling, and pelletizing it, and also using, as component B), at least one highly branched or hyperbranched polycarbonate B1) with an OH number of from 1 to 600 mg KOH/g of polycarbonate (to DIN 53240, Part 2), or at least one highly branched or hyperbranched polyester B2) of AxBy type, where x is at least 1.1 and y is at least 2.1, or a mixture of these.