  We study the low temperature dynamics in films made of molecular magnets, i.
e. crystals composed of molecules having large electronic spin S in their
ground state. The electronic spin dynamics is mediated by coupling to a nuclear
spin bath; this coupling allows transitions for a small fraction of electronic
spins between their two energy minima, Sz=+- S, under resonant conditions when
the change of the Zeeman energy in magnetic dipolar field of other electronic
spins is compensated by interaction with nuclear spins. Transitions of resonant
spins can result in opening or closing resonances in their neighbors leading to
the collective dynamics at sufficiently large density P0 of resonant spins. We
formulate and solve the equivalent dynamic percolation problem for the Bethe
lattice (BL) of spins interacting with z neighbors and find that depending on
the density of resonant spins P0 and the number of neighbors z the system has
either one (2<z<6) or two (z > 5) kinetic transitions at P_{0}=Pc1 ~
exp(-1/3)/(3z) and P0=Pc2 ~ exp(-1)/z. The former transition is continuous and
associated with the formation of an infinite cluster of coupled resonant spins
similarly to the static percolation transition occurring at P0 ~ 1/z. The
latter transition, z>5, is discontinuous and associated with the instantaneous
increase in the density of resonant spins from the small value ~ 1/z to near
unity. Experimental implications of our results are discussed.
