The current popular cosmological models have granted the population of dwarf satellite galaxies a key role: their number, location, and masses constrain both the distribution of dark matter and the physical evolution of their hosts. In the past years, there has been increasing observational evidence that objects with masses of dwarf galaxies can form in the tidal tails of colliding galaxies, as well as speculations that they could become satellite-like galaxies orbiting around their progenitors and thus be cosmologically important. Yet, whether the so-called "Tidal Dwarf Galaxy" (TDG) candidates are really long-lived objects and not transient features only present in young interacting systems is still largely an open question to which numerical simulations may give precise answers. We present here a set of 96 N-body simulations of colliding galaxies with various mass ratios and encounter geometries, including gas dynamics and star formation. We study the formation and long-term evolution of their TDG candidates. Among the 593 substructures initially identified in tidal tails, about 75% fall back onto their progenitor or are disrupted in a few 10⁸ years. The remaining 25% become long-lived bound objects that typically survive more than 2 Gyr with masses above 10⁸ M_&sun;. These long-lived, satellite-like objects, are found to form in massive gaseous accumulations originally located in the outermost regions of the tidal tails. Studying the statistical properties of the simulated TDGs, we infer several basic properties that dwarf galaxies should meet to have a possible tidal origin and apply these criteria to the Local Group dwarfs. We further found that the presence of TDGs would foster the anisotropy observed in the distribution of classical satellite galaxies around their host. Identifying the conditions fulfilled by interacting systems that were able to form long-lived tidal dwarfs - a spiral merging with a galaxy between 1/4 and 8 times its mass, on a prograde orbit, with an orbital plane inclined up to 40 degrees to the disk plane - and estimating their fraction as a function of redshift, we roughly estimate their contribution to the overall population of dwarfs. We conclude that a small but significant fraction of them - a few percent - could be of tidal origin. This number may be underestimated in particular environments such as the vicinity of early-type galaxies or in groups.