  We discuss the potential of a next generation space-borne CMB experiment for
studies of extragalactic sources with reference to COrE+, a project submitted
to ESA in response to the M4 call. We consider three possible options for the
telescope size: 1m, 1.5m and 2m (although the last option is probably
impractical, given the M4 boundary conditions). The proposed instrument will be
far more sensitive than Planck and will have a diffraction-limited angular
resolution. These properties imply that even the 1m telescope option will
perform substantially better than Planck for studies of extragalactic sources.
The source detection limits as a function of frequency have been estimated by
means of realistic simulations. The most significant improvements over Planck
results are presented for each option. COrE+ will provide much larger samples
of truly local star-forming galaxies, making possible analyses of the
properties of galaxies (luminosity functions, dust mass functions, star
formation rate functions, dust temperature distributions, etc.) across the
Hubble sequence. Even more interestingly, COrE+ will detect, at |b|> 30 deg,
thousands of strongly gravitationally lensed galaxies. Such large samples are
of extraordinary astrophysical and cosmological value in many fields. Moreover,
COrE+ high frequency maps will be optimally suited to pick up proto-clusters of
dusty galaxies, i.e. to investigate the evolution of large scale structure at
larger redshifts than can be reached by other means. Thanks to its high
sensitivity COrE+ will also yield a spectacular advance in the blind detection
of extragalactic sources in polarization. This will open a new window for
studies of radio source polarization and of the global properties of magnetic
fields in star forming galaxies and of their relationships with SFRs.
