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We study the fundamental magnetic states of disc-shaped ferromagnetic particles with a uniaxial anisotropy along the symmetry axis. Besides the monodomain, a bidomain state is also identified and studied both numerically and theoretically. This bidomain state in the symmetry broken system is the analog of the vortex state, consists of two coaxial oppositely magnetized cylindrically symmetric domains, and is stable at zero-bias field, unlike magnetic bubbles in ferromagnetic films. For a given disc thickness we find the critical radius above which the magnetization configuration falls into the bidomain bubble state. The critical radius depends strongly on the film thickness, especially for ultrathin films. In an external field the bidomain state remains stable over a range of field strengths. The switching from the bidomain to the monodomain takes place through an abrupt domain annihilation mechanism.