  We investigate the generic behaviour of marginally trapped tubes (roughly
time-evolved apparent horizons) using simple, spherically symmetric examples of
dust and scalar field collapse/accretion onto pre-existing black holes. We find
that given appropriate physical conditions the evolution of the marginally
trapped tube may be either null, timelike, or spacelike and further that the
marginally trapped two-sphere cross-sections may either expand or contract in
area. Spacelike expansions occur when the matter falling into a black hole
satisfies $\rho - P \leq 1/A$, where $A$ is the area of the horizon while
$\rho$ and $P$ are respectively the density and pressure of the matter.
Timelike evolutions occur when $(\rho - P)$ is greater than this cut-off and so
would be expected to be more common for large black holes. Physically they
correspond to horizon "jumps" as extreme conditions force the formation of new
horizons outside of the old.
