  The non-adiabatic quantum dynamics of the H+H$_2^+$ $\rightarrow$ H$_2$+
H$^+$ charge transfer reactions, and some isotopic variants, is studied with an
accurate wave packet method. A recently developed $3\times$3 diabatic potential
model is used, which is based on very accurate {\it ab initio} calculations and
includes the long-range interactions for ground and excited states. It is found
that for initial H$_2^+$(v=0), the quasi-degenerate H$_2$(v'=4) non-reactive
charge transfer product is enhanced, producing an increase of the reaction
probability and cross section. It becomes the dominant channel from collision
energies above 0.2 eV, producing a ratio, between v'=4 and the rest of v's,
that increases up to 1 eV. H+H$_2^+$ $\rightarrow$ H$_2^+$+ H exchange reaction
channel is nearly negligible, while the reactive and non-reactive charge
transfer reaction channels are of the same order, except that corresponding to
H$_2$(v'=4), and the two charge transfer processes compete below 0.2 eV. This
enhancement is expected to play an important vibrational and isotopic effect
that need to be evaluated. For the three proton case, the problem of the
permutation symmetry is discussed when using reactant Jacobi coordinates.
