  This review presents a comprehensive study of the spatial dispersion of
propagating magnons electrically emitted in extended yttrium-iron garnet (YIG)
films by the spin transfer effects across a YIG$\vert$Pt interface. Our goal is
to provide a generic framework to describe the magnon transconductance inside
magnetic films. We experimentally elucidate the relevant spectral contributions
by studying the lateral decay of the magnon signal. While most of the injected
magnons do not reach the collector, the propagating magnons can be split into
two-fluids: \textit{i)} a large fraction of high-energy magnons carrying energy
of about $k_B T_0$, where $T_0$ is the lattice temperature, with a
characteristic decay length in the sub-micrometer range, and \textit{ii)} a
small fraction of low-energy magnons, which are particles carrying energy of
about $\hbar \omega_K$, where $\omega_K/(2 \pi)$ is the Kittel frequency, with
a characteristic decay length in the micrometer range. Taking advantage of
their different physical properties, the low-energy magnons can become the
dominant fluid \textit{i)} at large spin transfer rates for the bias causing
the emission of magnons, \textit{ii)} at large distance from the emitter,
\textit{iii)} at small film thickness, or \textit{iv)} for reduced band
mismatch between the YIG below the emitter and the bulk due to variation of the
magnon concentration. This broader picture complements part I \cite{kohno_SD},
which focuses solely on the nonlinear transport properties of low-energy
magnons.
