  We explore the way different loop quantization prescriptions affect the
formation of trapped surfaces in the gravitational collapse of a homogeneous
dust cloud, with a particular emphasis on the so called $\mu_o$ scheme in which
loop quantum cosmology was initially formulated. Its undesirable features in
cosmological models led to the so-called improved dynamics or the $\bar \mu$
scheme. While the jury is still out on the right scheme for black hole
spacetimes, we show that as far as the black hole formation is concerned the
$\mu_o$ scheme has another, so far unknown, serious problem. We find that in
the $\mu_o$ scheme no trapped surfaces would form for a non-singular collapse
of a homogeneous dust cloud in the marginally bound case unless the minimum
non-zero area of the loops over which holonomies are computed or the
Barbero-Immirzi parameter decreases almost four times from its standard value.
It turns out that the trapped surfaces in the $\mu_o$ scheme for the marginally
bound case are also forbidden for any arbitrary matter content as long as the
collapsing interior is isometric to a spatially flat
Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetime. We find that in
contrast to the situation in the $\mu_o$ scheme, black holes can form in the
$\bar \mu$ scheme, and also other lattice refinements with a mass gap
determined by quantum geometry.
