  Decays of the lightest neutralino are studied in $R_p$-violating models, with
operators $\lambda^\prime L Q D^c$ and $\lambda L L E^c$ involving
third-generation matter fields and with dominant $\lambda^\prime$ and $\lambda$
couplings. Decays with the top-quark among the particles produced are
considered, in addition to those with an almost massless final state.
Phenomenological analyses for examples of both classes of decays are presented.
No specific assumption on the composition of the lightest neutralino is made.
Our formulae can easily be generalized to study decays of heavier neutralinos.
We also discuss effects of the $\rp$ decays of the $\tilde \chi_1^0$ on the
possible faking of the $H^\pm$ signal at the LHC by the recently pointed out
$\tilde \tau \bar b t$ production through $\lambda'_{333}$ coupling.
