The Gaia astrometric mission may offer an unprecedented opportunity to discover new tidal streams in the Galactic halo. To test this, we apply nGC3, a great-circle-cell count method that combines position and proper motion data to identify streams, to ten mock Gaia catalogues of K giants and RR Lyrae stars constructed from cosmological simulations of Milky Way analogues. We analyse two sets of simulations, one using a combination of $N$-body and semi-analytical methods which has extremely high resolution, the other using hydro-dynamical methods, which captures the dynamics of baryons, including the formation of an in situ halo. These ten realisations of plausible Galactic merger histories allow us to assess the potential for the recovery of tidal streams in different Milky Way formation scenarios. We include the Gaia~selection function and observational errors in these mock catalogues. We find that the nGC3 method has a well-defined detection boundary in the space of stream width and projected overdensity, that can be predicted based on direct observables alone. We predict that about 4-13 dwarf galaxy streams can be detected in a typical Milky Way-mass halo with Gaia+nGC3, with an estimated efficiency of $>$80% inside the detection boundary. The progenitors of these streams are in the mass range of the classical dwarf galaxies and may have been accreted as early as redshift $sim3$. Finally, we analyse how different possible extensions of the Gaia mission will improve the detection of tidal streams.
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