A technique has been developed to simultaneously determine recombination rate coefficients, alpha(e), and initial concentrations of ion types that coexist in a flowing afterglow plasma. This was tested using the H-3(+) + allene reaction in which two different C3H3+ isomers are produced. Use of an electrostatic Langmuir probe enabled the C3H3+ isomer branching ratios for propargyl and cyclic C3H3+ from this allene reaction and their alpha(e) to be determined over the temperature range 172-489 K. The study showed that the cyclic C3H3+ to propargyl C3H3+ branching ratios from the allene reaction varied from 50150 at 172 K to 18/82 at 489 K. Over this temperature range, the alpha(e) for both isomers change only slightly. The room temperature alpha(e) values for propargyl and cyclic C3H3+ are (1.15 +/- 0.2) x 10(-7) and (8.00 +/- 0.1) x 10(-7) cm(3)/s, respectively. The data are discussed relative to current theories and in relation to fuel-rich flame chemistry, interstellar molecular synthesis, and modeling of Titan's atmosphere.