  We show that an ansatz based on independent composite bosons [Phys. Rep. 463,
215 (2008)] accurately describes the condensate fraction of molecular
Bose-Einstein condensates in ultracold Fermi gases. The entanglement between
the fermionic constituents of a single Feshbach molecule then governs the
many-particle statistics of the condensate, from the limit of strong
interaction to close to unitarity. This result strengthens the role of
entanglement as the indispensable driver of composite-boson behavior. The
condensate fraction of fermion pairs at zero temperature that we compute
matches excellently previous results obtained by means of fixed-node diffusion
Monte Carlo methods and the Bogoliubov depletion approximation. This paves the
way towards the exploration of the BEC-BCS crossover physics in mixtures of
cold Fermi gases with an arbitrary number of fermion pairs as well as the
implementation of Hong-Ou-Mandel-like interference experiments proposed within
coboson theory.
