Hyperbranched partly cross‐linked polycyclotrimers of 1,4‐diethynylbenzene, 2,6‐diethynylnaphthalene, and 2,6‐diethynylanthracene, Pc(1,4‐DEB), Pc(2,6‐DEN), and Pc(2,6‐DEA), respectively, are prepared using TaCl5/Ph4Sn catalyst. Brunauer–Emmett–Teller (BET) surface area, microporosity, and maximum sorption capacity for H2 and CO2 decrease in the order of decreasing relative content of branching points in polycyclotrimers Pc(1,4‐DEB) > Pc(2,6‐DEN) > Pc(2,6‐DEA), the highest values for Pc(1,4‐DEB) being SBET = 1299 m2 g−1, aH2 = 1.26 wt% (100 kPa, 77 K), and aCO2 = 10.8 wt% (100 kPa, 273 K). N2 isotherms show that adsorption/desorption hysteresis occurs already at low equilibrium pressures. CO2 isotherms show that the time allotted to the measurement influences both the maximum adsorption capacity and the hysteresis upon desorption.