My PhD thesis is entitled Boundaries of slices of quasifuchsian space. As well as the results from my paper it has some conjectural results about the boundary of the Maskit and Bers slices. On the basis of very strong numerical evidence, I conjecture that the boundary spirals infinitely almost everywhere and that the Hausdorff dimension of the Maskit slice is less than 1.25 (and more likely to be closer to 1.05). You can download it in PDF (1.8MB) format only. The computer programs that come with are available on this page. In order to save some trees, the version on this page is a single spaced version with small margins, unlike the printed version which is double spaced with large margins. In order to save space on my webpage, this version doesn't have the highest quality versions of some of the figures produced by David Wright. If you're interested, email me or him.
Below is a series of zooms into the Maskit slice, clockwise from top left to bottom right, illustrating the phenomenon of spirals in the boundary of the Maskit slice.