We present a detailed analysis of the partial coverage of the broad line region of Q1232+082 (z_em = 2.57) by an intervening H₂-bearing cloud at z_abs = 2.3377. Using curve of growth analysis and line profile fitting, we demonstrate that the H₂-bearing component of the cloud covers the QSO intrinsic continuum source completely but only part of the Broad Line Region (BLR). We find that only 48±6 % of the CIV BLR emission is covered by the CI gas. We suggest several possible explanations for this partial coverage: binary quasars, gravitational lensing, and small size of the intervening cloud, the most likely being the latter. We estimate the number densities in the cloud: n_H2 ∼ 110 cm⁻³ for the H₂-bearing core and n_H2 ∼ 30 cm⁻³ for the neutral envelope. We derive the linear size of the H₂-bearing core and the neutral envelope along the line of sight to be l_H2=0.15^+0.05_−0.05 pc and l_HI = 8.2^+6.5_−4.1 pc. Assuming that the H₂-bearing core is spherical in shape, we estimate a typical size of the CIV BLR to be ∼ 0.2 pc. The large size we derive for the neutral cloud extent together with the covering factor of ∼94% of the Lyman-alpha emission means that the Lyman-alpha BLR is probably fully covered but that the emission extends well beyond the limits of the BLR. Assuming the CIV BLR is virialized, we derive the mass of the central back-hole M_BH = 6.8^+4.1_−4.5× 10⁸ M_Sun.

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