Complete and detailed experimental transition probability density functions P(E＇,E) have been determined for the first time for collisions between a large, highly vibrationally excited molecule, toluene, and several bath gases. This was achieved by applying the method of kinetically controlled selective ionization (KCSI) (Paper I [J. Chem. Phys. 112, 4076 (2000), preceding article]). An optimum P(E-＇,E) representation is recommended (monoexponential with a parametric exponent in the argument) which uses only three parameters and features a smooth behavior of all parameters for the entire set of bath gases. In helium, argon, and CO2 the P(E-＇,E) show relatively increased amplitudes in the wings-large energy gaps \E＇-E\-which can also be represented by a biexponential form. The fractional contribution of the second exponent in these biexponentials, which is directly related to the fraction of the so-called "supercollisions," is found to be very small (< 0.1%). For larger colliders the second term disappears completely and the wings of P(E-＇,E) have an even smaller amplitude than that provided by a monoexponential form. At such low levels, the second exponent is therefore of practically no relevance for the overall energy relaxation rate. All optimized P(E-＇,E) representations show a marked linear energetic dependence of the (weak) collision parameter alpha(1)(E), which also results in an (approximately) linear dependence of and of the square root of . The energy transfer parameters presented in this study form a new benchmark class in certainty and accuracy, e.g., with only 2%-7% uncertainty for our data below 25 000 cm(-1). They should also form a reliable testground for future trajectory calculations and theories describing collisional energy transfer of polyatomic molecules. (C) 2000 American Institute of Physics. [S0021-9606(00)01604-4].