  We show by extensive simulations that the whole supercritical phase of the
three-dimensional uniform forest model simultaneously exhibits an infinite tree
and a rich variety of critical phenomena. Besides typical scalings like
algebraically decaying correlation, power-law distribution of cluster sizes,
and divergent correlation length, a number of anomalous behaviors emerge. The
fractal dimensions for off-giant trees take different values when being
measured by linear system size or gyration radius. The giant-tree size displays
two-length scaling fluctuations, instead of following the central-limit
theorem.
