We present simulations of the formation of thick disks via the accretion of two-component satellites onto a pre-existing thin disk. Our goal is to establish the detailed characteristics of the thick disks obtained in this way, as well as their dependence on the initial orbital and internal properties of the accreted objects. We find that mergers with 10-20% mass of the mass of the host lead to the formation of thick disks whose characteristics are similar, both in morphology as in kinematics, to those observed. Despite the relatively large mass ratios, the host disks are not fully destroyed by the infalling satellites: a remaining kinematically cold and thin component containing ~15-25% of the mass can be identified, which is embedded in a hotter and thicker disk. This may for example, explain the existence of a very old thin disk stars in the Milky Way. The final scale-heights of the disks depend both on the initial inclination and properties of the merger, but the fraction of satellite stellar particles at ~4 scale-heights directly measures the mass ratio between the satellite and host galaxy. Our thick disks typically show boxy isophotes at very low surface brightness levels (>6 magnitudes below their peak value). Kinematically, the velocity ellipsoids of the simulated thick disks are similar to that of the Galactic thick disk at the solar radius. The trend of sigma_Z/sigma_R with radius is found to be a very good discriminant of the initial inclination of the accreted satellite. In the Milky Way, the possible existence of a vertical gradient in the rotational velocity of the thick disk as well as the observed value of sigma_Z/sigma_R at the solar vicinity appear to favour the formation of the thick disk by a merger with either low or intermediate orbital inclination.
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