The invention concerns a biocompatible polymer having a mole weight more than 50000 g/mole, preferably 90000 g/mole for fixing biological ligands comprising at least a first linear segment consisting of a hydrophobic homopolymer derived from polymerisation of a hydrophobic monomer A; a second linear segment consisting of a hydrophilic polymer derived from copolymerisation of a monomer B bearing a reactive function X and a hydrophilic monomer C not bearing any reactive function, said second segment being covalently bound to one end of the first segment. The invention also concerns a biological polymer-ligand-conjugate, a device for capturing a target molecule comprising a solid support whereon is immobilised a biological polymer-ligand conjugate and methods for preparing said polymer. The invention is mainly applicable in the field of diagnosis.