  We investigate the quantum dynamics of wave packets in a class of decorated
lattices, both quasiperiodic and random, where a nominal quasi-one
dimensionality is introduced at local levels, bringing in a deterministic or
even random variations in the distribution of the coordination number
throughout the system. We show that certain correlations in the numerical
values of the system Hamiltonian can cause a drastic change in the dynamical
evolution of the wave packet, revealing a complete delocalization, independent
of the energy of the travelling particle, even in the absence of any
translational invariance. We use an exact decimation of a selected subset of
the degrees of freedom, and an analysis of the commutation of the $2 \times 2$
transfer matrices on a renormalized version of the parent systems within a
tight binding framework. An in-depth analysis of the mean square displacement,
temporal autocorrelation function and the inverse participation ratio
establishes the gross change in the behaviour of the wave packet dynamics. The
consequence is the occurrence of a parameter-driven insulator-metal transition
over the full (or a major) range of the energy spectrum in each case. In
certain cases, inclusion of an external magnetic flux enables us to control the
transition. The observation is general, and, to our mind, can inspire
experiments involving photonics or matter wave localization.
