  We consider Anzellotti-type almost minimizers for the thin obstacle (or
Signorini) problem with zero thin obstacle and establish their $C^{1,\beta}$
regularity on the either side of the thin manifold, the optimal growth away
from the free boundary, the $C^{1,\gamma}$ regularity of the regular part of
the free boundary, as well as a structural theorem for the singular set. The
analysis of the free boundary is based on a successful adaptation of energy
methods such as a one-parameter family of Weiss-type monotonicity formulas,
Almgren-type frequency formula, and the epiperimetric and logarithmic
epiperimetric inequalities for the solutions of the thin obstacle problem.
