  We study the role of size effects on atomic collapse of charged impurity in
the flat band system. The tight-binding simulations are made for the dice
lattice with circular quantum dot shapes. It is shown that the mixing of in-gap
edge states with bound states in impurity potential leads to increasing the
critical charge value. This effect, together with enhancement of gap due to
spatial quantization, makes it more difficult to observe the
dive-into-continuum phenomenon in small quantum dots. At the same time, we show
that if in-gap states are filled, the resonant tunneling to bound state in the
impurity potential might occur at much smaller charge, which demonstrates
non-monotonous dependence with the size of sample lattice. In addition, we
study the possibility of creating supercritical localized potential well on
different sublattices, and show that it is possible only on rim sites, but not
on hub site. The predicted effects are expected to naturally occur in
artificial flat band lattices.
