Porous pillared graphene oxide (GO) materials were prepared using solvothermal reaction of Hummers GO with solution of Tetrakis(4-aminophenyl)methane (TKAm) in methanol. The intercalation of TKAm molecules between individual GO sheets, performed under swelling condition, results in expansion of inter-layer distance of GO from ~ 7.5 Å to 13-14 Å. Pillaring GO with bulky, rigid 3D shaped TKAm molecules could be an advantage for the preparation of stable pillared structures compared to e.g. aliphatic or aromatic diamines. Insertion of TKAm molecules into inter-layer space of GO results in formation of interconnected network of sub-nanometer slit pores. The expanded GO structure prepared with optimized GO/TKAm composition shows Specific Surface Area (SSA) up to 660 m2/g which is among the highest reported for GO materials pillared using organic spacers. Modelling of GO structures pillared with TKAm molecules shows that maximal SSA of about 2300 m2/g is theoretically possible for realistic concentration of pillaring molecules in GO interlayers. Hydrogen sorption by pillared GO/TKAm is found to follow standard correlation with SSA both at ambient and liquid nitrogen temperatures with highest uptakes of 1.66 wt% achieved at 77 K and 0.25 wt% at 295 K. Our theoretical simulations show that pillared GO structures do not provide improvement of hydrogen storage beyond well-established physisorption trends even for idealized materials with subnanometer pores and SSA of 2300 e3700 m2/g.