  Composite bosons made of two bosonic constituents exhibit deviations from
ideal bosonic behavior due to their substructure. This deviation is reflected
by the normalization ratio of the quantum state of N composites. We find a set
of saturable, efficiently evaluable bounds for this indicator, which quantifies
the bosonic behavior of composites via the entanglement of their constituents.
We predict an abrupt transition between ordinary and exaggerated bosonic
behavior in a condensate of two-boson composites.
