  We revise the long studied problem of fluctuation conductivity (FC) in
disordered two-dimensional superconductors placed in a perpendicular magnetic
field by finally deriving the complete solution in the temperature-magnetic
field phase diagram. The obtained expressions allow both to perform
straightforward (numerical) calculation of the FC surface
$\delta\sigma_{xx}^{(\mathrm{tot})}(T,H)$ and to get asymptotic expressions in
all its qualitatively different domains. This surface becomes in particular
non-trivial at low temperatures, where it is trough-shaped with $%
\delta\sigma_{xx}^{(\mathrm{tot})}(T,H)<0$. In this region, close to the
quantum phase transition,
$\delta\sigma_{xx}^{(\mathrm{tot})}(T,H=\mathrm{const})$ is non-monotonic, in
agreement with experimental findings. We reanalyzed and present comparisons to
several experimental measurements. Based on our results we derive a qualitative
picture of superconducting fluctuations close to $H_{\mathrm{c2}}(0) $ and T=0
where fluctuation Cooper pairs rotate with cyclotron frequency
$\omega_{c}\sim\Delta_{\mathrm{BCS}}^{-1}$ and Larmor radius $\sim
\xi_{\mathrm{BCS}}$, forming some kind of quantum liquid with long coherence
length $\xi_{\mathrm{QF}}\gg\xi_{\mathrm{BCS}}$ and slow relaxation
($\tau_{\mathrm{QF}}\gg\hbar\Delta_{\mathrm{BCS}}^{-1}$).
