  We study topological open membranes of BF type in a manifest BV formalism.
Our main interest is the effect of the bulk deformations on the algebra of
boundary operators. This forms a homotopy Lie algebra, which can be understood
in terms of a closed string field theory. The simplest models are associated to
quasi-Lie bialgebras and are of Chern-Simons type. More generally, the induced
structure is a Courant algebroid, or ``quasi-Lie bialgebroid'', with boundary
conditions related to Dirac bundles. A canonical example is the topological
open membrane coupling to a closed 3-form, modeling the deformation of strings
by a C-field. The Courant algebroid for this model describes a modification of
deformation quantization. We propose our models as a tool to find a formal
solution to the quantization problem of Courant algebroids.
