  Place an active particle at the root of the infinite $d$-ary tree and dormant
particles at each non-root site. Active particles move towards the root with
probability $p$ and otherwise move to a uniformly sampled child vertex. When an
active particle moves to a site containing dormant particles, all the particles
at the site become active. The critical drift $p_d$ is the infimum over all $p$
for which infinitely many particles visit the root almost surely. We give
improved bounds on $\sup_{d \geq m} p_d$ and prove monotonicity of critical
values associated to a self-similar variant.
