  We investigate heat current magnification due to asymmetry in the number of
spins in two-branched classical and quantum spin systems. We begin by studying
the classical Ising like spin models using Q2R and CCA dynamics and show that
just the difference in the number of spins is not enough and some other source
of asymmetry is required to observe heat current magnification. Unequal
spin--spin interaction strength in the upper and lower branch is employed as a
source of this asymmetry and it proves adequate for generating current
magnification in both the models. Suitable physical motivation is then provided
for current magnification in these systems, along with ways to control and
manipulate magnification through various system parameters. We also study a
five spin Quantum system with modified Heisenberg XXZ interaction and preserved
magnetisation using the Redfield master equation. We show that it is possible
to generate current magnification in this model by the asymmetry in the number
of spins only. Our results indicate that the onset of current magnification is
accompanied by a dip in the total current flowing through the system. On
analysis it is revealed that this dip might occur because of the intersection
of two non-degenerate energy levels for certain values of the asymmetry
parameter in the modified XXZ model. We deduce that the additional degeneracy
and the ergodic constraint due to fixed magnetisation in the system are the
main reasons for current magnification and other atypical behaviors observed.
We then use the concept of `ergotropy' to support these findings. Finally, for
both the classical and quantum models, we see that current magnification is
only observed when temperature gradient and intra-system interaction strength
have similar order of energy.
