Synthesis of hyperbranched poly(arylene ether phosphine oxide)s, HB PAEPOs, from bis(4-fluorophenyl)(4-hydroxyphenyl)phosphine oxide, la, in the presence of a series of core molecules with systematically altered reactivity of the aryl fluoride groups provides polymers with molecular weights, MWs, controlled by the concentration of the core molecule, and narrow polydispersity indices, PDIs. Polymers with number-average molecular weights ranging from 3270 to 8100 Da, and PDIs as low as 1.25 have been prepared. The core molecules utilized in this work consist of a series of fluorinated triarylphosphine oxides, tris(4-fluorophenyl)phosphine oxide, tris(3,4-difluorophenyl)phosphine oxide, and tris(3,4,5-trifluorophenyl)phosphine oxide, 2a, 2b, and 2c, respectively. The most highly activated core, 2c, provides the best control over the final MW and the lowest PDIs. The degree of branching, DB, for the HB PAEPOs decreases from 0.57 with no core to below 0.40 at higher concentrations of 2b and 2c.