We analyze HST and ground based spectra of the brightest BALQSO in the UV: PG~0946+301. A detailed study of the absorption troughs as a function of velocity is presented, facilitated by the use of a new algorithm to solve for the optical depth as a function of velocity for multiplet lines. We find convincing evidence for saturation in parts of the troughs. This supports our previous assertion that saturation is common in BALs and therefore cast doubts on claims for very high metallicity in BAL flows. Due to the importance of BAL saturation we also discuss its evidence in other objects. In PG~0946+301 large differences in ionization as a function of velocity are detected and our findings supports the hypothesis that the line of sight intersects a number of flow components that combine to give the appearance of the whole trough. Based on the optical depth profiles, we develop a geometrical-kinematical model for the flow. We have positively identified 16 ions of 8 elements (H~I, C~III, C~IV, N~III, N~IV, N~V, O~III, O~IV, O~V, O~VI, Ne~V, Ne~VIII, P~V, Si~IV, S~V, S~VI) and have a probable identifications of Mg~X and S~IV. Unlike earlier analysis of IUE data, we find no evidence for BALs arising from excited ionic states in the HST spectrum of PG~0946+301.