(Abridged) The upper atmospheres of close-in gas giant exoplanets are subjected to intense heating/tidal forces from their parent stars. Atomic/ionized hydrogen (H) layers are sufficiently rarefied that magnetic pressure may dominate gas pressure for expected planetary magnetic field strength. We examine the magnetospheric structure using a 3D isothermal magnetohydrodynamic model that includes: a static "dead zone" near the magnetic equator containing magnetically confined gas; a "wind zone" outside the magnetic equator in which thermal pressure gradients and the magneto-centrifugal-tidal effect give rise to transonic outflow; and a region near the poles where sufficiently strong tidal forces may suppress transonic outflow. Using dipole field geometry, we estimate the size of the dead zone to be ~1-10 planetary radii for a range of parameters. To understand appropriate base conditions for the 3D isothermal model, we compute a 1D thermal model in which photoelectric heating from the stellar Lyman continuum is balanced by collisionally-excited Lyman �� cooling. This 1D model exhibits a H layer with temperatures T=5000-10000K down to pressures of 10-100 nbar. Using the 3D isothermal model, we compute H column densities and Lyman �� transmission spectra for parameters appropriate to HD 209458b. Line-integrated transit depths of 5-10% can be achieved for the above base conditions. Strong magnetic fields increase the transit signal while decreasing the mass loss, due to higher covering fraction and density of the dead zone. In our model, most of the transit signal arises from magnetically confined gas, some of which may be outside the L1 equipotential. Hence the presence of gas outside the L1 equipotential does not directly imply mass loss. Lastly, we discuss the domain of applicability for the magnetic wind model described in this paper and in the Roche-lobe overflow model.

26 pages, 17 figures (5 color), 2 appendices; submitted to ApJ; higher resolution version available at http://www.astro.virginia.edu/~gbt8f/HotJupMag_fullres_astroph.pdf