  The theory of growth kinetics developed previously is extended to the
asymmetric case of off-critical quenches for systems with a conserved scalar
order parameter. In this instance the new parameter $M$, the average global
value of the order parameter, enters the theory. For $M=0$ one has critical
quenches, while for sufficiently large $M$ one approaches the coexistence
curve. For all $M$ the theory supports a scaling solution for the order
parameter correlation function with the Lifshitz-Slyozov-Wagner growth law $L
\sim t^{1/3}$. The theoretically determined scaling function depends only on
the spatial dimensionality $d$ and the parameter $M$, and is determined
explicitly here in two and three dimensions. Near the coexistence curve
oscillations in the scaling function are suppressed. The structure factor
displays Porod's law $Q^{-(d+1)}$ behaviour at large scaled wavenumbers $Q$,
and $Q^{4}$ behaviour at small scaled wavenumbers, for all $M$. The peak in the
structure factor widens as $M$ increases and develops a significant tail for
quenches near the coexistence curve. This is in qualitative agreement with
simulations.
