  Minute-timescale TeV flares have been observed in several blazars. The fast
flaring requires compact regions in the jet that boost their emission towards
the observer at an extreme Doppler factor of delta>50. For TeV photons to avoid
annihilation in the broad line region of PKS 1222+216, the flares must come
from large (pc) scales challenging most models proposed to explain them. Here
we elaborate on the magnetic reconnection minijet model for the blazar flaring,
focusing on the inherently time-dependent aspects of the process of magnetic
reconnection. I argue that, for the physical conditions prevailing in blazar
jets, the reconnection layer fragments leading to the formation a large number
of plasmoids. Occasionally a plasmoid grows to become a large, "monster"
plasmoid. I show that radiation emitted from the reconnection event can account
for the observed "envelope" of ~ day-long blazar activity while radiation from
monster plasmoids can power the fastest TeV flares. The model is applied to
several blazars with observed fast flaring. The inferred distance of the
dissipation zone from the black hole and the typical size of the reconnection
regions are R_diss~0.3-1 pc and l' \simless 10^{16} cm, respectively. The
required magnetization of the jet at this distance is modest: sigma ~a few.
Such dissipation distance R_diss and reconnection size l' are expected if the
jet contains field structures with size of the order of the black-hole horizon.
