  Magnetohydrodynamic (MHD) theory and simulations have shown that reconnection
is triggered via a fast "ideal" tearing instability in current sheets whose
inverse aspect ratio decreases to $a/L\sim S^{-1/3}$, with $S$ is the Lundquist
number defined by the half-length $L$ of the current sheet (of thickness $2a$).
Ideal tearing, in 2D sheets, triggers a hierarchical collapse via stretching of
X-points and recursive instability. At each step, the local Lundquist number
decreases, until the subsequent sheet thickness either approaches kinetic
scales or the Lundquist number becomes sufficiently small. Here we carry out a
series of Hall-MHD simulations to show how the Hall effect modifies recursive
reconnection once the ion inertial scale is approached. We show that as the ion
inertial length becomes of the order of the inner, singular layer thickness at
some step of the recursive collapse, reconnection transits from the
plasmoid-dominant regime to an intermediate plasmoid+Hall regime and then to
the Hall-dominant regime. The structure around the X-point, the reconnection
rate, the dissipation property and the power spectra are also modified
significantly by the Hall effect.
