Black hole binary transients undergo dramatic evolution in their X-ray timing and spectral behaviour during outbursts. In recent years a paradigm has arisen in which soft X-ray states are associated with an inner disc radius at, or very close to, the innermost stable circular orbit (ISCO) around the black hole, while in hard X-ray states the inner edge of the disc is further from the black hole. Models of advective flows suggest that as the X-ray luminosity drops in hard states, the inner disc progressively recedes, from a few to hundreds gravitational radii. Recent observations which show broad iron line detections and estimates of the disc component strength suggest that a non-recessed disc could still be present in bright hard states. In this study we present a comprehensive analysis of the spectral components associated with the inner disc, utilising data from instruments with sensitive low-energy responses and including reanalyses of previously published results. A key component of the study is to fully estimate systematic uncertainties by e.g. investigating in detail the effect of having a hydrogen column density that is fixed or free to vary. We conclude that for L_x > 0.01 of the Eddington limit, spectral fits allow us to constrain the disc to be < 10R_g. There is, however, clear evidence that when L_x is between 10^-2-- 10^-3 Eddington, the disc does begin to recede. We include measurements of disc radii in two quiescent black hole binaries, and present the inferred evolution of accretion parameters in the entire range of bolometric luminosities 10^-8 -- 1 Eddington. We compare our results with theoretical models and note that the implied rate of disc recession with luminosity is consistent with recent empirical results on the X-ray timing behaviour of black holes of all masses.
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