Ab initio G3(MP2,CC)//B3LYP/6-311G** calculations have been performed to investigate the potential energy surface (PES) and mechanism of the reaction of phenyl radical with propylene followed by kinetic RRKM-ME calculations of rate constants and product branching ratios at various temperatures and pressures. The reaction can proceed either by direct hydrogen abstraction producing benzene and three C3H5 radicals [1-propenyl (CH3CHCH), 2-propenyl (CH3CCH2), and allyl (CH2CHCH2)] or by addition of phenyl to the CH or CH2 units of propylene followed by rearrangements on the C9H11 PES producing nine different products after H or CH3 losses. The H abstraction channels are found to be kinetically preferable at temperatures relevant to combustion and to contribute 55-75% to the total product yield in the 1000-2000 K temperature range, with the allyl radical being the major product (similar to 45%). The relative contributions of phenyl addition channels are calculated to be similar to 35% at 1000 K, decreasing to similar to 15% at 2000 K, with styrene + CH3 and 3-phenylpropene + H being the major products. Collisional stabilization of C6H5 + C3H6 addition complexes is computed to be significant only at temperatures up to 1000-1200 K, depending on the pressure, and maximizes at low temperatures of 300-700 K reaching up to 90% of the total product yield. At T > 1200 K collisional stabilization becomes negligible, whereas the dissociation products, styrene plus methyl and 3-phenylpropene + H, account for up to 45% of the total product yield. The production of bicyclic aromatic species including indane C9H10 is found to be negligible at all studied conditions indicating that the phenyl addition to propylene cannot be a source of polycyclic aromatic hydrocarbons (PAN) on the C9H11 PES. Alternatively, the formation of a PAH molecule, indene C9H8, can be accomplished through secondary reactions after activation of a major product of the C6H5 + C3H6 addition reaction, 3-phenylpropene, by direct hydrogen abstraction by small radicals, such as H, OH, CH3, etc. It is shown that at typical combustion temperatures 77-90% of C9H9 radicals formed by H-abstraction from 3-phenylpropene undergo a closure of a cyclopentene ring via low barriers and then lose a hydrogen atom producing indene. This results in 7.0-14.5% yield of indene relative to the initial C6H5 + C3H6 reactants within the 1000 2000 K temperature range.