In 1993, Choptuik discovered the critical phenomenon associated with the collapse of a spherical shell of minimally coupled massless scalar matter fields. Most interestingly, he found that black holes with infinitesimally small mass can form in such a classical collapse. It is, however, known that quantum gravitational effects cannot be neglected for black holes of Planckian size. In fact, in 2D dilaton gravity, which has many similarities with spherically symmetric 4D Einstein gravity, we have shown that Choptuik's scaling law breaks down when quantum effects are included [<a href=''http://arxiv.org/abs/gr-qc/9606152''>Bose:1996pi</a>, <a href=''http://arxiv.org/abs/gr-qc/9608040''>Peleg:1996ce</a>]. a strong possibility for the existence of a lower bound (of Planckian order) on the mass of black holes formed from such a collapse. In other words, it appears that a quantum pressure (analogous to the fermionic degeneracy pressure that can arise in a stellar collapse) prevents the formation of black holes with mass smaller than that of Planckian order. An investigation of the effect of quantum corrections in the more realistic and involved scenario of such collapses in general relativity is pending.