The "room problem" refers to the question of the origin of the physical space into which the granite or other batholith has intruded. Generally there is no place for the ascending mass of magma to intrude, unless it first removes the material in its path. Stoping, the spalling of sidewall and roof rocks into the molten magma, has been suggested as an explanation of the process of migration upwards through the overlying strata. But stoping, which does occur to a limited degree in many igneous processes [and some sedimentary and metamorphic ones as well (salt migration and marblization of limestone are two examples)] cannot make more than a minor contribution to solving the room problem, since the stoping materials only add further to the volume of the granite. Furthermore, stoping of the cold wall rock into the magma body will soon cool the magma below the point of melting the wall rock. Since granitic magmas are far cooler than basic magmas, stoping will not get you very far!
The physical evidence we do see for stoping is the presence of xenoliths, remnants of the surrounding wall rock incorporated in the pluton. But xenoliths are almost never a major component of batholiths. If they were, the composition of the batholith itself would change drastically, since the amount of wall rock removed would have to equal the volume of the batholith in order to even partially alleviate the room problem.
At present there is no satisfactory explanation for the room problem during emplacement of a pluton.
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2010 Arthur V. Chadwick, Ph.D.