We generalize the construction of connected branched polymers and the notion of the volume of the space of connected branched polymers studied by Brydges and Imbrie (Ann Math, 158:1019–1039, 2003), and Kenyon and Winkler (Am Math Mon, 116(7):612–628, 2009) to any central hyperplane arrangement $$\mathcal{A }$$ . The volume of the resulting configuration space of connected branched polymers associated to the hyperplane arrangement $$\mathcal{A }$$ is expressed through the value of the characteristic polynomial of $$\mathcal{A }$$ at 0. We give a more general definition of the space of branched polymers, where we do not require connectivity, and introduce the notion of q-volume for it, which is expressed through the value of the characteristic polynomial of $$\mathcal{A }$$ at $$-q$$ . Finally, we relate the volume of the space of branched polymers to broken circuits and show that the cohomology ring of the space of branched polymers is isomorphic to the Orlik–Solomon algebra.