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The most famous advocate for non growth or steady state growth is Herman Daly. Daly's theories underline much of Ecological Economics and Biophysical Economics. They also inform significant parts of Sustainability studies and Complexity Economics, particularly Allometric Growth Theory.

Daly was the graduate student of Georgescu-Roegen who did early influential work examining the 2nd Law of Thermodynamics and it's relationship to human economies.
Another early advocate of steady state economies was systems ecologist Howard Odum who was an influential figure in BioPhysical Economics, a branch of ecological economics. Energy and the Wealth of Nations is pretty close to a textbook for the BioPhysical Econ approach to growth by Odum's student Charles Hall.
Another famous example is Meadows et. al. and the Limits to Growth Models. These models provoked heated debate and many economists challenged the implications of the models. Robert Solow challenged the Meadows team based on assumptions derived from Neo-Classical Growth theory. However a number of subsequent studies have found the assumptions of Solow's model problematic* and use systems theory approaches based on energy and entropic pollution that are much closer in approach to the Meadows system theory model. The Meadows team were able to model a scenario run with a steady state outcome provided "the steady state is achieved by applying population control policies (maximum 2 children per couple in the world), improvements in food production (eg organic food), stabilization of industrial production per capita, control policies for pollution, soil erosion and depletion protocol of nonrenewable resources.". However, Meadows now feels that the policy reforms would have had to have been undertaken long ago and this outcome is no longer achievable.
Hotelling's framework for non-renewable resource extraction was used to critique the Meadow's model. While the Hotelling model is often taught and underlines current thinking on discount rates it has been shown not to hold to empirical data.. Meadow's model by contrast has a high correlation between the Standard Run Scenario and observed data from the 30 years since it's publication.

*Recent Papers Critical of NeoClassical Growth Theory Ayres Warr http://www.insead.edu/facultyresearch/research/doc.cfm?did=1244 Cleveland http://www.peakoil.net/files/biophysical%20constraints%20to%20economic%20growth%20by%20Cleveland.pdf Brown et al. http://biology.unm.edu/jHBrown/Documents/Publications/2000s/2011-1%20Energetic%20Limits%20to%20Economic%20Growth.pdf
One of the more interesting growth theories to come out in recent years is Allometric Growth Theory which is centred in the research team of West, Bettencourt, Brown, Moses from the Santa Fe Institute. Their theory says that growth is physiological rather than psychological. Cities and businesses have many of the same properties of biological networks so if we model these institutions as though they were organisms we can use one of the few constants of biology, Kiebers law to predict growth based on metabolic energy use. One of the interesting insights of this approach is that business growth appears to follow growth pattern close to natural growth (Kleiber's Law is stated as a 3/4 power law or 75% and business growth seems to follow about 80% (p0.8) growth rate). Since both of these growth rates will follow a sigmoidal curve (they will grow rapidly, plateau, and die) they can be considered sustainable in an energetic understanding of the term. Cities, however, have a superlinear growth exponent (about 1.15) meaning that the curve will at some point go vertical and the system will collapse. Again this approach finds a strong relationship between metabolic energy consumption and growth.
In terms of the end game nothing in my five years of research on the subject suggests that sustained growth is possible given the underlying energy flow rates that are achievable with existing technology and current policy. In a best case scenario sustained economic contraction will prompt an orderly degrowth agenda with movement towards dramatically lower energy consumption, low energy farming, restorative agriculture and non-coercive population control policies. Really what this entails is reducing energy consumption to the levels of about 1960's France. However, given the time frames orderly degrowth is probably not achievable without a large scale mobilization similar to the War Effort of the 1940's. By most accounts demand for oil will exceed supply flow rates at some point between 2015 and 2030. The impacts of Climate Change exceeding important thresholds could begin as soon as 2050 but almost certainly will be felt by 2100. As well important environmental limits on nitrogen pollution, ecosystem degradation, species loss, biological diversity, have been exceeded. Given the inability of politicians to formulate a coherent policy response and they very small impacts of green initiatives on energy consumption, ecosystem degration and entropic pollution the end game could be quite disruptive.