Abstract: A polycondensation reactor for processing low viscosity polyester or another polymer into relatively highly viscosity polymer comprises a substantially cylindrical horizontal reactor vessel with a polymer inlet and a polymer outlet adjacent its opposite ends and a vapor exhaust opening in the upper side of the vessel at its outlet end. A polymer agitator is rotated axially within the chamber and includes plural alternating annular overflow and underflow baffles and multiple perforated film-forming screens disposed therebetween in parallel spaced relation to one another. The overflow baffles are in peripheral polymer-sealing relation to the vessel while the underflow baffles have multiple underflow recesses in their outer peripheries, whereby the baffles define a tortuous polymer flow path alternately through their respective polymer overflow and underflow openings to control residence time, distribution and viscosity growth as the polymer flows between the baffles.