  The evolution of the low temperature electronic structure of the cuprate
metals from the overdoped to the underdoped side has recently been addressed
through Angle-Dependant Magneto-Resistance (ADMR) experiments in
La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$. The results show a striking difference
between hole dopings $p = 0.24$ and $p = 0.21$ which lie on either side of a
putative quantum critical point at intermediate $p$. Motivated by this, we here
study the theory of ADMR in correlated layered materials, paying special
attention to the role of angle dependent quasiparticle weights
$Z_{\mathbf{k}}$. Such a $Z_{\mathbf{k}}$ is expected to characterize a number
of popular models of the cuprate materials, particularly when underdoped.
Further, in the limit of weak interlayer hopping the quasiparticle weight will
affect the $c$-axis transport measured in ADMR experiments. We show that proper
inclusion of the quasiparticle weight does not support an interpretation of the
data in terms of a $(\pi, \pi)$ spin density wave ordered state, in agreement
with the lack of direct evidence for such order. We show that a simple model of
Fermi surface reconfiguring across a van Hove point captures many of the
striking differences seen between $p = 0.21$ and $p = 0.24$. We comment on why
such a model may be appropriate for interpreting the ADMR data, despite having
a large Fermi surface at $p = 0.21$, seemingly in contradiction with other
evidence for a small Fermi surafce at that doping level.
