The present work is concerned with the weak interactions between hydrogen and halogen molecules, i. e. the interactions of pairs H₂-X₂ with X=F, Cl, Br, which are dominated by dispersion and quadrupole-quadrupole forces. The global minimum of the four dimensional CCSD(T) pair potentials is always a T shaped structure where H₂ acts as the hat of the T, with dissociation energies D_e of 1.3, 2.4 and 3.1 kJ/mol for F₂, Cl₂ and Br₂, respectively. MP2/AVQZ results, in reasonable agreement with CCSD(T) results extrapolated to the basis set limit, are used for detailed scans of the potentials. Due to the large difference in the rotational constants of the monomers, in the adiabatic approximation, one can solve the rotational Schrödinger equation for H₂ in the potential of the X₂ molecule. This yields effective two dimensional rotationally adiabatic potential energy surfaces where pH₂ and oH₂ are point-like particles. These potentials for the H₂-X₂ complexes have global and local minima for effective linear and T-shaped complexes, respectively, which are separated by 0.4-1.0 kJ/mol, where oH₂ binds stronger than pH₂ to X₂, due to higher alignment to minima structures of the 4D-pair potential. Further, we provide fits of an analytical function to the rotationally adiabatic potentials.