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We perform a detailed finite-size scaling analysis of the sheet resistance inBi-films and the LaAlO$_{3}$/SrTiO$_{3}$ interface in the presence and absenceof a magnetic field applied perpendicular to the system. Our main aim is toexplore the occurrence of Berezinskii-Kosterlitz-Thouless (BKT) and quantumphase transition behavior in the presence of limited size, stemming from thefinite extent of the homogeneous domains or the magnetic field. Moreover weexplore the implications thereof. Above an extrapolated BKT transitiontemperature, modulated by the thickness $d$, gate voltage $%V_{g}$ or magneticfield $H$, we identify a temperature range where BKT behavior occurs. Its rangeis controlled by the relevant limiting lengths,which are set by the extent ofthe homogeneous domains or the magnetic field. The extrapolated BKT transitionlines $T_{c}\left(d,V_{g},H\right) $ uncover compatibility with the occurrenceof a quantum phase transition where $T_{c}\left( d_{c},V_{gc},H_{c}\right) =0$.However, an essential implication of the respective limiting length is that theextrapolated phase transition lines $T_{c}\left( d,V_{g},H\right) $ areunattainable. Consequently, given a finite limiting length, BKT and quantumphase transitions do not occur. Nevertheless, BKT and quantum critical behavioris observable, controlled by the extent of the relevant limiting length.Additional results and implications include: the magnetic field induced finitesize effect generates a flattening out of the sheet resistance in the$T\rightarrow 0$ limit, while in zero field it exhibits a characteristictemperature dependence and vanishes at $T=0$ only. The former prediction isconfirmed in both, the Bi-films and the LaAlO$_{3}$/SrTiO$_{3}$ interface, aswell as in previous studies. The latter is consistent with theLaAlO$_{3}$/SrTiO$_{3}$ interface data, while the Bi-films exhibit a flatteningout.

Suppression of the Berezinskii-Kosterlitz-Thouless and Quantum Phase Transitions in 2D Superconductors by Finite Size Effects