We employ the full-potential linearized augmented plane-wave method to report a systematic density-functional theory study of the magnetic properties of the 3d transition-metal (V, Cr, Mn, Fe, Co, and Ni) monolayers deposited on the Rh(100) substrate. We find that all monolayer films are magnetic. The size of the local magnetic moments across the transition-metal series follows Hund's rule with a maximum magnetic moment of 3.77μ B for Mn. The largest induced magnetic moment of about 0.46μ B was found for Rh atoms adjacent to the Co film. When relaxations are included, we predict a ferromagnetic (FM) ground state for V, Co, and Ni, while Cr, Mn, and Fe favor a c(2 × 2)antiferromagnetic (AFM) state, a checkerboard arrangement of up and down magnetic moments. The magnetic anisotropy energies of these ultrathin magnetic films are calculated for the FM and AFM states. With the exception of Cr, the easy axis of the magnetization is predicted to be in the film plane. Rough estimates of the ordering temperatures are given. To gain an understanding of the c(2 × 2) AFM state of Fe/Rh(100), we analyze this result with respect to the trends of the magnetic order of 3d monolayers on other 4d substrates, such as Pd(100) and Ag(100).