  We investigate universal behavior in the recombination rate of three bosons
close to threshold. Using the He-He system as a reference, we solve the
three-body Schr\"odinger equation above the dimer threshold for different
potentials having large values of the two-body scattering length $a$. To this
aim we use the hyperspherical adiabatic expansion and we extract the $S$-matrix
through the integral relations recently derived. The results are compared to
the universal form, $\alpha\approx 67.1\sin^2[s_0\ln(\kappa_*a)+\gamma]$, for
different values of $a$ and selected values of the three-body parameter
$\kappa_*$. A good agreement with the universal formula is obtained after
introducing a particular type of finite-range corrections, which have been
recently proposed by two of the authors in Ref.[1]. Furthermore, we analyze the
validity of the above formula in the description of a very different system:
neutron-neutron-proton recombination. Our analysis confirms the universal
character of the process in systems of very different scales having a large
two-body scattering length.
