We present a detailed analysis of the partial coverage of the Q1232+082 (zem= 2.57) broad-line region (BLR) by an intervening H2-bearing cloud at zabs= 2.3377. Using curve of growth analysis and line profile fitting, we demonstrate that the H2-bearing component of the cloud covers the quasi-stellar object (QSO) intrinsic continuum source completely but only part of the BLR. We find that only 48 +/- 6 per cent of the C iv BLR emission is covered by the C i absorbing gas. We observe residual light (similar to 6 per cent) as well in the bottom of the O i 1302 absorption from the cloud, redshifted on top of the QSO Lyman a emission line. Therefore, the extent of the neutral phase of the absorbing cloud is not large enough to cover all of the background source. The most likely explanation for this partial coverage is the small size of the intervening cloud, which is comparable to the BLR size. We estimate the number densities in the cloud: similar to 110 cm(-3) for the H2-bearing core and nH similar to 30 cm-3 for the neutral envelope. Given the column densities, N(H2) = 3.71 +/- 0.97 x 1019 cm-2 and N(H i) = 7.94 +/- 1.6 x 1020 cm(-2), we derive the linear size of the H2-bearing core and the neutral envelope along the line of sight to be similar to 0.15+0.05-0.05 pc and similar to 8.2(-4.1)(+6.5) pc, respectively. We estimate the size of the C iv BLR by two ways: (i) extrapolating sizeluminosity relations derived from reverberation observations and (ii) assuming that the H2-bearing core and the BLR are spherical in shape and the results are similar to 0.26 and similar to 0.18 pc, respectively. The large size we derive for the extent of the neutral phase of the absorbing cloud together with a covering factor of similar to 0.94 of the Lyman a emission means that the Lyman a BLR is probably fully covered but that the Lyman a emission extends well beyond the limits of the BLR.