We propose a distributed implementation for integrated sensing and communication (ISAC) backed by a massive multiple input multiple output (CF-mMIMO) architecture without cells. Distributed multi-antenna access points (APs) simultaneously serve communication users (UEs) and emit probing signals towards multiple specified zones for sensing. The APs can switch between communication and sensing modes, and adjust their transmit power based on the network settings and sensing and communication operations' requirements. By considering local partial zero-forcing and maximum-ratio-transmit precoding at the APs for communication and sensing, respectively, we first derive closed-form expressions for the spectral efficiency (SE) of the UEs and the mainlobe-to-average-sidelobe ratio (MASR) of the sensing zones. Then, a joint operation mode selection and power control design problem is formulated to maximize the SE fairness among the UEs, while ensuring specific levels of MASR for sensing zones. The complicated mixed-integer problem is relaxed and solved via successive convex approximation approach. We further propose a low-complexity design, where AP mode selection is designed through a greedy algorithm and then power control is designed based on this chosen mode. Our findings reveal that the proposed scheme can consistently ensure a sensing success rate of $100\%$ for different network setups with a satisfactory fairness among all UEs.

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