Sensor networks are mainly used to gather strategic information in various monitored areas. Sensors may be deployed in zones where their internal memory, or the sensors themselves, can be corrupted. Since deployed sensors cannot be easily replaced, network persistence and robustness are the two main issues that have to be addressed while efficiently deploying large scale sensor networks. The goal of forming a Minimum Connected Cover of a query region in sensor networks is to select a subset of nodes that entirely covers a particular monitored area, which is strongly connected, and which does not contain a subset with the same properties. In this paper, we consider the general case, wherein every sensor has a different sensing and communication radius. We propose two novel and robust solutions to the minimum connected cover problem that can cope with both transient faults (corruptions of the internal memory of sensors) and sensor crash/join. Also, our proposal includes extended versions which use multi-hop information. Our algorithms use small atomicity (i.e., each sensor reads variables of only one of its neighbors at a time). Our solutions are self ∗  (self-configuration, self-stabilization, and self-healing). Via simulations, we conclude that our solutions provide better performance, in terms of coverage, than pre-existing self-stabilizing solutions. Moreover, we observe that multi-hop solutions produce a better approximation to an optimal cover set.