What is difference between Bose-Einstein condensation in 3D and 2D? I read in the reference [1] below that

An infinite, non-interacting two-dimensional gas of bosons has no phase transition and never develops spontaneous coherence. However, adding interactions leads to the Berezhinski-Kosterlitz-Thouless(BKT) transition, below which power law correlations, and super fluidity can develop. For a finite, trapped two-dimensional system of non-interacting particles, macroscopic occupation of a single particle state can also occur.

This article is regarding the Condensation of Exciton-polariton which has been considered as 2D Bose Einstein condensate.
This means, if we introduce interaction (trapping potentials) in a finite 2D system, it can undergo a phase transition that is similar to BE condensate. But I thought even a 3D bosonic system requires a trapping potential so that they can occupy a quantized energy levels and reach the critical phase space density to undergo the macroscopic occupation. In this respect, how is 2D condensate different from 3D condensate ? Also, reference [2] emphasizes similar requirement for BKT in 2D. Can anyone explain what point I am missing here. Any comments are highly appreciated. Thanks
[1] J. Kasprzak et al., Nature 443, 409 (2006)
[2] D. S. Petrov, M. Holzmann and G. V. Shlyapnikov, Phys.
Rev. Lett. 84, 2551 (2000)
 A: In principle you can get a condensate in an infinite 3D system. In practice however it is problematic, as the requirement is that you need a certain finite density and therefore an infinite number of atoms. That's why you introduce a trap to make your system finite and get away and obtain BEC with finite number of atoms.
In 2D however you can't have a condensate in an extended system in principle at non-zero temperature (as any other long-range order; see "Mermin-Wagner theorem"), because fluctuations smear out the order entirely for any dimension $D \leq2$ (footnote: if you ask what is the significance of D=2, I am tempted to say it is the power $n=2$ of the gradient term in the free energy expansion $F(\phi) \propto |\nabla \phi|^2+...$).
Nevertheless the divergences in D=2 are very weak (logarithmic) therefore, therefore in finite systems all Mermin-Wagner-like phenomena are exponentially suppressed, and hence can be ignored for most practical purposes (like graphene people who seemingly are never bothered by the fact that their sample are not supposed to exist at finite temperatures).
