  We study the condensed phase of a Bose-Fermi mixture with a tunable pairing
interaction between bosons and fermions with many-body diagrammatic methods and
fixed-node diffusion Quantum Monte Carlo simulations. A universal behavior of
the condensate fraction and bosonic momentum distribution with respect to the
boson concentration is found to hold in an extended range of boson-fermion
couplings and concentrations. For vanishing boson density, we prove that the
bosonic condensate fraction reduces to the quasiparticle weight Z of the Fermi
polaron studied in the context of polarized Fermi gases, unifying in this way
two apparently unrelated quantities.
