The purpose of this article is to characterize the Fréchet spaces \(F\) which appear as a quotient of the space \(A(\Omega)\) of the complex valued real analytic functions defined on an open subset \(\Omega\) of \(\mathbb R^d\). The paper continues investigations of several authors about the structural theory of the space \(A(\Omega)\). In their important article in [Stud. Math. 142, No. 2, 187--200 (2000; Zbl 0990.46015)], \textit{P. Domanski} and \textit{D. Vogt} showed that every quotient of \(A(\Omega)\) which is a Fréchet space satisfies the restrictive topological invariant \((\overline{\overline{\Omega}})\) of Vogt. This was an important step in the proof that \(A(\Omega)\) has no Schauder basis. At the time when that article was written, the only known infinite-dimensional Fréchet quotient of \(A(\Omega)\) was the countable product of copies of the field of complex numbers. In [Arch. Math. 81, 208--214 (2003; Zbl 1048.46028)], they showed that there is a nuclear Köthe sequence space \(\lambda_ 1(B)\) with a continuous norm which is a quotient of \(A(\Omega)\) for every open set \(\Omega\). The main result of the present article states that a Fréchet space \(F\) is isomorphic to a quotient of \(A(\Omega)\) for some (or any) open subset \(\Omega\) of \(\mathbb R^d\) if and only if it satisfies the property \((\overline{\overline{\Omega}})\) and it is \(n^{1/d}\)-nuclear, or equivalently, if and only if \(E\) has \((\overline{\overline{\Omega}})\) and is isomorphic to a quotient of \(H(D^d)\), the space of holomorphic functions on the \(d\)-dimensional polydisc. An essential step is the characterization of those Fréchet spaces \(F\) such that \(\text{Ext}^1(A(\Omega),F)=0\), a result which is of independent interest.