  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.
