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We have used pulsed magnetic fields up to 60Tesla to suppress thecontribution of superconducting fluctuations(SCF)to the conductivity above Tcin a series of YBa2Cu3O6+x from the deep pseudogapped state to slightoverdoping. Accurate determinations of the SCF conductivity versus temperatureand magnetic field have been achieved. Their joint quantitative analyses withrespect to Nernst data allow us to establish that thermal fluctuationsfollowing the Ginzburg-Landau(GL) scheme are dominant for nearly optimallydoped samples. The deduced coherence length xi(T) is in perfect agreement witha gaussian (Aslamazov-Larkin) contribution for 1.01Tc<T<1.2Tc. A phasefluctuation contribution might be invoked for the most underdoped samples in aT range which increases when controlled disorder is introduced by electronirradiation. For all dopings we evidence that the fluctuations are highlydamped when increasing T or H. The data permits us to define a field Hc^primeand a temperature Tc^prime above which the SCF are fully suppressed. Theanalysis of the fluctuation magnetoconductance in the GL approach allows us todetermine the critical field Hc2(0). The actual values of Hc^prime(0) andHc2(0) are found quite similar and both increase with hole doping. Thesedepairing fields, which are directly connected to the magnitude of the SC gap,do therefore follow the Tc variation which is at odds with the sharp decreaseof the pseudogap T* with increasing hole doping. This is on line with ourprevious evidence that T* is not the onset of pairing. We finally propose athree dimensional phase diagram including a disorder axis, which allows toexplain most peculiar observations done so far on the diverse cuprate families.

High Field Studies of Superconducting Fluctuations in High-T_c Cuprates: Evidence for a Small Gap distinct from the Large Pseudogap