The present invention relates to a star-shaped polymer M comprising a central core and n arms attached to the core, wherein each arm is a polymer chain comprising at least one polymer PI, wherein n is an integer greater than or equal to 4, characterized in that each polymer chain is independently functionalized at its end by a group G chosen from a (meth)acrylate group, a catechol derivative, a phenylboronic acid derivative and a pyrogallolyl group, on condition that at least one polymer chain is functionalized at its end by a catechol derivative, a phenylboronic acid derivative or a pyrogallolyl group. The present invention also relates to a crosslinked polymer obtained by crosslinking at least one star-shaped polymer M as defined above, and the use thereof as self-healing material and/or as bioadhesive material, notably as surgical glue or as a medical device or in a medical device. The present invention also relates to a method for correcting a defect of a material comprising, notably consisting essentially of, a crosslinked polymer according to the invention.