  We extend to the gamut of functional forms of the probability distribution of
the time-dependent step-length a previous model dubbed Elephant Quantum Walk,
which considers a uniform distribution and yields hyperballistic dynamics where
the variance grows cubicly with time, $\sigma ^2 \propto t^3$, and a Gaussian
for the position of the walker. We investigate this proposal both locally and
globally with the results showing that the time-dependent interplay between
interference, memory and long-range hopping leads to multiple transitions
between dynamical regimes, namely ballistic $\rightarrow$ diffusive
$\rightarrow$ superdiffusive $\rightarrow$ ballistic $\rightarrow$
hyperballistic for non-hermitian coin whereas the first diffusive regime is
quelled for implementations using the Hadamard coin. In addition, we observe a
robust asymptotic approach to maximal coin-space entanglement.
