Stabilization of H-3(+) collision complexes has been studied at nominal temperatures between 11 and 33 K using a 22-pole radio frequency (rf) ion trap. Apparent binary rate coefficients, k* = k(r) + k(3)[H-2], have been measured for para- and normal-hydrogen at number densities between some 10(11) and 10(14) cm(-3). The state specific rate coefficients extracted for radiative stabilization, k(r)(T-ij), are all below 2 x 10(-16) cm(3) s(-1). There is a slight tendency to decrease with increasing temperature. In contrast to simple expectations, k(r)(11 K-ij) is for j = 0 a factor of 2 smaller than for j = 1. The ternary rate coefficients for p-H-2 show a rather steep T-dependence; however, they are increasing with temperature. The state specific ternary rate coefficients, k(3)(T-ij), measured for j = 0 and derived for j = 1 from measurements with n-H-2, differ by an order of magnitude. Most of these surprising observations are in disagreement with predictions from standard association models, which are based on statistical assumptions and the separation of complex formation and competition between stabilization and decay. Most probably, the unexpected collision dynamics are due to the fact that, at the low translational energies of the present experiment, only a small number of partial waves participate. This should make exact quantum mechanical calculations of k(r) feasible. More complex is three-body stabilization, because it occurs on the H-5(+) potential energy surface.