  The properties of a two-dimensional low density (n<<1) electron system with
strong onsite Hubbard attraction U>W (W is the bandwidth) in the presence of a
strong random potential V uniformly distributed in the range from -V to +V are
considered. Electronic hoppings only at neighboring sites on the square lattice
are taken into account, thus W=8t. The calculations were carried out for a
lattice of 24x24 sites with periodic boundary conditions. In the framework of
the Bogoliubov - de Gennes approach we observed an appearance of inhomogeneous
states of spatially separated Fermi-Bose mixture of Cooper pairs and unpaired
electrons with the formation of bosonic droplets of different size in the
matrix of the unpaired normal states We observed a decrease in the droplet size
(from larger droplets to individual bielectronic pairs) when we decrease the
electron density at fixed values of the Hubbard attraction and random
potential. The obtained results are important for the construction of the gross
phase diagram and understanding of the nature of the phase transition between
superconducting, normal metallic and localized states in quasi-2D (thin) film
of a dirty metal. In a more practical sense it is interesting also for the
experimental implementation of superconducting qubits on quantum circuits with
high impedances in granular superconductors.
