We analyze vertical structures where a regulated network operator serves n network users, and the network users compete in quantities for customers. We distinguish two cases: (i) none of the network users are related to the network operator (ownership unbundling), (ii) one of the network users is partially integrated with the operator and the others are disintegrated (legal unbundling). We seek to understand when ownership unbundling leads to lower customer prices, and formalize necessary conditions. In general, legal unbundling implies a less effective regulation, but it reduces the degree of market distortion caused by the difference between marginal costs and average costs (= regulated prices of network usage). We find that the necessary condition is not satisfied for realistic values of the relevant parameters, i.e. legal unbundling leads to lower costumer prices than ownership unbundling in most relevant markets.