Hollow atoms in which the $K$ shell is empty while the outer shells are populated allow studying a variety of important and unusual properties of atoms. The diagram x-ray emission lines of such atoms, the ${K}^{h}{\ensuremath{\alpha}}_{1,2}$ hypersatellites (HSs), were measured for the $3d$ transition metals, $Z=23--30$, with a high energy resolution using photoexcitation by monochromatized synchrotron radiation. Good agreement with ab initio relativistic multiconfigurational Dirac-Fock calculations was found. The measured HS intensity variation with the excitation energy yields accurate values for the excitation thresholds, excludes contributions from shake-up processes, and indicates domination near threshold of a nonshake process. The $Z$ variation of the HS shifts from the diagram line $K{\ensuremath{\alpha}}_{1,2}$, the ${K}^{h}{\ensuremath{\alpha}}_{1}\ensuremath{-}{K}^{h}{\ensuremath{\alpha}}_{2}$ splitting, and the ${K}^{h}{\ensuremath{\alpha}}_{1}/{K}^{h}{\ensuremath{\alpha}}_{2}$ intensity ratio, derived from the measurements, are also discussed with a particular emphasis on the QED corrections and Breit interaction.