Crossed molecular beam experiments on dicarbon and tricarbon reactions with unsaturated hydrocarbons acetylene, methylacetylene, and ethylene were performed to investigate the dynamics of channels leading to hydrogen-deficient hydrocarbon radicals. In the light of the results of new ab initio calculations, the experimental data suggest that these reactions are governed by an initial addition of C2/C3 to the pi molecular orbitals forming highly unsaturated cyclic structures. These intermediates are connected via various transition states and are suggested to ring open to chain isomers which decompose predominantly by displacement of atomic hydrogen, forming C4H, C5H, HCCCCCH2, HCCCCCCH3, H2CCCCH and H2CCCCCH. The C2(1 sigma g+) + C2H4 reaction has no entrance barrier and the channel leading to the H2CCCCH product is strongly exothermic. This is in strong contrast with the C3(1 sigma g+) + C2H4 reaction as this is characterized by a 26.4 kJ mol-1 threshold to form a HCCCCCH2 isomer. Analogous to the behavior with ethylene, preliminary results on the reactions of C2 and C3 with C2H2 and CH3CCH showed the H-displacement channels of these systems to share many similarities such as the absence/presence of an entrance barrier and the reaction mechanism. The explicit identification of the C2/C3 vs. hydrogen displacement demonstrates that hydrogen-deficient hydrocarbon radicals can be formed easily in environments like those of combustion processes. Our work is a first step towards a systematic database of the intermediates and the reaction products which are involved in this important class of reactions. These findings should be included in future models of PAH and soot formation in combustion flames.