We consider conformations and intramolecular conformational transitions in amphiphilic starlike polymers formed by diblock copolymer arms with inner hydrophobic and outer polyelectrolyte blocks. A combination of an analytical mean-field theory with the assumption free numerical self-consistent field (SCF) modeling approach is applied. It is demonstrated that unimolecular micelles with collapsed hydrophobic cores and swollen polyelectrolyte coronae are formed in dilute aqueous solutions at high ionic strength or/and low degree of ionization of the outer hydrophilic block. An intramolecular conformational transition related to the unfolding of the hydrophobic core of the unimolecular micelles can be triggered by a decrease in the ionic strength of the solution or/and increase in the degree of ionization of the coronal blocks. In the stars with large number of diblock copolymer arms the transition between conformations with collapsed or stretched core-forming blocks occurs continuously by progressive unfolding of the core domain. By contrast, in the stars with relatively small number of arms the continuous unfolding of the core is interrupted by an abrupt unravelling transition. A detailed SCF analysis indicates that under both unfolding scenarios the arms of the star are extended fairly equally; i.e., no intramolecular disproportionation occurs.