Disclosed herein are globular nanostructures having a hydrodynamic diameter (Dh) of 8-100 nm comprising a central part and a peripheral part, wherein said central part has a calculated diameter (Dc) of 6-90 nm and said peripheral part has an estimated thickness (Tp) so that Dh=Dc+2Tp, wherein said central part comprises: (i) a crosslinked polymeric framework comprising monomer residues wherein at least 30 % by number of the monomer residues have crosslinked thereby forming the crosslinked polymeric framework and/or (ii) a branched polymeric framework comprising monomer residues wherein the number of branch points is at least 30 % of the number of monomer residues, wherein said central part comprises chelating groups of which at least 4 allow chelation of at least one multiply charged cation, wherein said chelating groups are independently selected from the group consisting of-COOR1, -P=O(OR1)(OR2), and -S(=O)2OR1, wherein R1 and R2 are independently selected from the group consisting of a negative charge, H, and lower alkyls, and wherein said peripheral part comprises a synthetic polymer material covalently attached to the central part, wherein the synthetic polymer material is hydrophilic and bioinert, and electrically neutral or zwitterionic. Also disclosed are compositions comprising such nanoparticles, and optionally also a radionuclide, use of such compositions, kits containing such compositions and methods for obtaining such compositions.