A strong quasistationary magnetic field is generated in hollow targets with curved internal surface under the action of a relativistically intense picosecond laser pulse. Experimental data evidence the formation of quasistationary strongly magnetized plasma structures decaying on a hundred picoseconds timescale, with the magnetic field strength of the kilotesla scale. Numerical simulations unravel the importance of transient processes during the magnetic field generation and suggest the existence of fast and slow regimes of plasmoid evolution depending on the interaction parameters. The proposed setup is suited for perspective highly magnetized plasma application and fundamental studies.