We show [74,75] that in the limit of large and positive
atom-atom scattering length the properties of an atomic-molecular
Bose-Einstein Condensate (amBEC) are determined by an universal
energy density functional (EDF). We find that the optimal conditions
for the formation of a stable amBEC are in the regime where there are
no shallow trimers and the atom-dimer scattering length is negative
and comparable in magnitude with the atom-atom scattering length. At
temperatures lower than 
the chemical potentials for the atoms
and molecules can be specified independently. Besides three-body
recombinations processes into dimers of large size, inelastic
processes involving the formation of deeply bound small size molecular
states are possible. These inelastic processes do not lead to an
efficient heating of the amBEC and can be used for its mostly
non-destructive monitoring.