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Transmission control protocol (TCP) is the most widely used transport protocol in today's Internet. Despite the fact that several mechanisms have been presented in recent literature to improve TCP, there remain some vexing attributes that impair TCPs performance. This paper addresses the issue of the efficiency and fairness of TCP in multihops satellite constellations. It mainly focuses on the effect of the change in flows count on TCP behavior. In case of a handover occurrence, a TCP sender may be forced to be sharing a new set of satellites with other users resulting in a change of flows count. This paper argues that the TCP rate of each flow should be dynamically adjusted to the available bandwidth when the number of flows that are competing for a single link, changes over time. An explicit and fair scheme is developed. The scheme matches the aggregate window size of all active TCP flows to the network pipe. At the same time, it provides all the active connections with feedbacks proportional to their round-trip time values so that the system converges to optimal efficiency and fairness. Feedbacks are signaled to TCP sources through the receiver's advertised window field in the TCP header of acknowledgments. Senders should accordingly regulate their sending rates. The proposed scheme is referred to as explicit and fair window adjustment (XFWA). Extensive simulation results show that the XFWA scheme substantially improves the system fairness, reduces the number of packet drops, and makes better utilization of the bottleneck link.