In this paper an extension of a behavioural subset of UML statecharts for mobile computations is proposed. We study collections of UML objects whose behaviour is given by statecharts. Each object resides in a given place, and a collection of such places forms a network. Objects are aware of the localities of other objects, i.e. the logical names of the places where the latter reside, but not of the physical name of such places. In addition to their usual capabilities, such as sending messages etc., objects can move between places and create and destroy places, which may result in a deep reconfiguration of the network. A formal semantics is presented for this mobility extension which builds upon a core semantics definition of statecharts without mobility which we have used successfully in several contexts in the past years. An example of a model of a network service which exploits mobility for resource usage balance is provided using the proposed extension of UML statecharts.