  We study quantum dynamics of a wave packet on a class of one dimensional
decorated aperiodic lattices, described within a tight binding formalism. We
look for the possibility of finding extended single particle states even in the
absence of any translational periodicity. The chosen lattices are stubbed with
one or more atoms, tunnel coupled to the backbone, thereby introducing a
minimal quasi-one dimensionality. It is seen that, for a group of such lattices
a certain correlation between the numerical values of the hopping amplitudes
leads to a complete delocalization of single particle states. In some other
cases, a special value of a magnetic flux trapped in the loops present in the
geometries delocalize the states, leading to a flux driven insulator to metal
transition. The mean square displacement, temporal autocorrelation function,
the time dependence of the inverse participation ratio, or the information
entropy - the so-called hallmarks of studying localization based on dynamics -
all of them indicate such a complete turnover in the nature of the single
particle states and the character of the energy spectrum under suitable
conditions. The results shown in this work using quasiperiodic lattices of the
Fibonacci family are much more general and hold good even for a randomly
disordered arrangement of the building blocks of the systems considered, and
indicate a subtle universality class under which these lattices can be grouped.
