  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.
