Distributed data processing over networks has received a lot of attention due to its wide applicability. In this paper, we consider the multitask problem of in-network distributed estimation. For the multitask problem, the unknown parameter vectors (tasks) for different nodes can be different. Moreover, considering some real application scenarios, it is also assumed that there are some similarities among the tasks. Thus, the intertask cooperation is helpful to enhance the estimation performance. In this paper, we exploit an additional special characteristic of the vectors of interest, namely, joint sparsity, aiming to further enhance the estimation performance. A distributed jointly sparse multitask algorithm for the collaborative sparse estimation problem is derived. In addition, an adaptive intertask cooperation strategy is adopted to improve the robustness against the degree of difference among the tasks. The performance of the proposed algorithm is analyzed theoretically, and its effectiveness is verified by some simulations.