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Investigation and characterization of exoplanetary magnetic elds and their role in evolution and habitability of planetary systems is closely connected with the study of the whole complex of stellar - planetary interactions, including stellar wind plasma flows, radiation, stellar and planetary gravity eects. A key element in the proposed approach is to take into account self- consistently the upper atmosphere of a close orbit giant exoplanet (so called Hot Jupiter) as an expanding dynamical gas layer heated and ionized by the stellar XUV radiation. Interaction of the outflowing plasma with the rotating planetary magnetic dipole eld leads to development of a current-carrying magnetodisk surrounding the exoplanet. The magnetic eld and electric current system associated with magnetodisk play crucial role in shaping and scaling of the Hot Jupiter's magnetosphere resulting in a slower than the-dipole-type decrease of the magnetic eld with the distance. That causes 40%-70% larger magnetosphere scales expected for Hot Jupiters as compared to those traditionally estimated by only the planetary dipole taken into account. The talk will summarize our recent theoretical and experimental results regarding development of a generalized model of an exoplanetary magnetosphere with the consequent account of the eects of an expanding upper atmospheric material and formation of an equatorial magnetodisk. The outcomes of the performed theoretical, experimental, and numerical studies contribute deeper understanding of exoplanetary mass loss process and related problem of magnetospheric protection of Hot Jupiters.