I feel tree maps are a very effective way of representing hierarchical data. Schneiderman has a very effective design that makes full use of a 2D rectangular space. I also agree with the authors that allowing the users to interact and control which nodes to expand, what data to display, how further to drill down enhances and quicken the users' comprehension. In terms of spatial utilization, I liked the way the authors have brought out the wastage of space in representing hierarchical by Venn diagrams and traditional tree structures. Mapping the content to the display seems to be a tricky area as the notion of depicting classification by color, hue, saturation comes in picture. The paper also reviews algorithms for drawing and tracking tree map structures.
In my opinion, tree maps become less effective when the hierarchies being visualized become too complex or detailed. A limited rectangular space getting divided into incomprehensible small divisions is not effective. Also, labeling becomes a problem and it becomes difficult to associate the visualization with data or hard numbers. An interesting alternative to this could be 3D tree maps. A paper based on this idea was introduced and a short abstract and further link can be found here: http://www.mendeley.com/research/magic-treemap-cube-visualizing-olympic-games-data/
The six faces represent six co-relating hierarchies and the users can explore these by rotating the cubed treemap as a whole. It can also be expanded into a 2D Cartesian system individually for inspection. This seemed an interesting extension of the tree map concept to me.
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