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Boson stars are considered as promising candidates for black hole mimickers.Similar to other compact objects they can form accretion disks around them. Theproperties of these disks could possibly distinguish them from other compactobjects like black holes in future observations. Retrograde thick disks aroundboson stars and the influence of strong magnetic fields on them were alreadystudied and it was shown that they can harbor very distinct features comparedto black hole disks. However, the case of prograde thick disks is mostlyunexplored, since they may appear much more similar to black hole disks. Inthis work we will investigate similarities and differences regarding progradethick disks around non-selfinteracting rotating boson stars and rotating blackholes. We assume thereby a polytropic equation of state and a constant specificangular momentum distribution of the disks. We classify the various conceivableboson star and black hole solutions by a dimensionless spin parameter $a$ andcompare their corresponding disk solutions. The influence of toroidal magneticfields on the disks is analyzed by selected disk properties, as the rest-massdensity distribution and the Bernoulli parameter. Disk solutions arecharacterized by their degree of magnetization represented by the magnetizationparameter $\beta_{mc}$. We found that strong magnetic fields can strengthen thedifferences of disk solutions or oppositely even lead to a correlation in diskproperties, depending on the spin parameter of the boson star and black holesolutions. We identify the vertical thickness of the boson star disks as themain differentiating factor, since for most solutions the vertical densitydistribution is far more outreaching for boson star disks compared to blackhole disks.

Comparison of Magnetized Thick Disks around Black Holes and Boson Stars