We present a statistical observational study of the tidal dwarf (TD) population in the nearby Universe by exploiting a large, homogeneous catalogue of galaxy mergers compiled from the Sloan Digital Sky Survey. 95 per cent of TD-producing mergers involve two spiral progenitors (typically both in the blue cloud), while most remaining systems have at least one spiral progenitor. The fraction of TD-producing mergers where both parents are early-type galaxies is less than 2 per cent, suggesting that TDs are unlikely to form in such mergers. The bulk of TD-producing mergers inhabit a field environment and have mass ratios greater than ∼1:7 (the median value is 1:2.5). TDs forming at the tidal-tail tips are ∼4 times more massive than those forming at the base of the tails. TD stellar masses are less than 10 per cent of the stellar masses of their parents (the median is 0.6 per cent) and lie within 15 optical half-light radii of their parent galaxies. The TD population is typically bluer than the parents, with a median offset of ∼0.3 mag in the (g − r) colour and the TD colours are not affected by the presence of active galactic nuclei (AGN) activity in their parents. An analysis of their star formation histories indicates that TDs contain both newly formed stars (with a median age of ∼30 Myr) and old stars drawn from the parent discs, each component probably contributing roughly equally to the stellar mass of the object. Thus TDs are not formed purely through gas condensation in tidal tails but host a significant component of old stars from the parent discs. Finally, an analysis of the TD contribution to the observed dwarf-to-massive galaxy ratio in the local Universe indicates that ∼6 per cent of dwarfs in nearby clusters may have a tidal origin, if TD production rates in nearby mergers are representative of those in the high-redshift Universe. Even if TD production rates at high redshift were several factors higher, it seems unlikely that the entire dwarf galaxy population today is a result of merger activity over the lifetime of the Universe.