Context. This is the third of a series of papers devoted to study in detail and with high-angular resolution intermediate-mass molecular outflows and their powering sources. Aims. The aim of this paper is to study the intermediate-mass YSO IRAS 20050+2720 and its molecular outflow, and put the results of this and the previous studied sources in the context of intermediate-mass star formation. Methods. We carried out VLA observations of the 7 mm continuum emission, and OVRO observations of the 2.7 mm continuum emission, CO(1-0), C18O(1-0), and HC3N(12-11) to map the core towards IRAS 20050+2720. The high-angular resolution of the observations allowed us to derive the properties of the dust emission, the molecular outflow, and the dense protostellar envelope. By adding this source to the sample of intermediate-mass protostars with outflows, we compare their properties and evolution with those of lower mass counterparts. Results. The 2.7mm continuum emission has been resolved into three sources, labeled OVRO 1, OVRO 2, and OVRO 3. Two of them, OVRO 1 and OVRO 2, have also been detected at 7 mm. OVRO 3, which is located close to the C18O emission peak, could be associated with IRAS 20050+2720. The mass of the sources, estimated from the dust continuum emission, is 6.5 Msun for OVRO 1, 1.8 Msun for OVRO 2, and 1.3 Msun for OVRO 3. The CO(1-0) emission traces two bipolar outflows within the OVRO field of view, a roughly east-west bipolar outflow, labeled A, driven by the intermediate-mass source OVRO 1, and a northeast-southwest bipolar outflow, labeled B, probably powered by a YSO engulfed in the circumstellar envelope surrounding OVRO 1.
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