The metric-affine gauge theory of gravity provides a broad framework in which
gauge theories of gravity can be formulated. In this article we fit
metric-affine gravity into the covariant BRST--antifield formalism in order to
obtain gauge fixed quantum actions. As an example the gauge fixing of a general
two-dimensional model of metric-affine gravity is worked out explicitly. The
result is shown to contain the gauge fixed action of the bosonic string in
conformal gauge as a special case.Comment: 19 pages LATEX, to appear in Phys. Rev.