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We consider a distribution of conductance fluctuations in quantum dots withsingle channel leads and continuous level spectra and we demonstrate that ithas a distinctly non-Gaussian shape and strong dependence on time-reversalsymmetry, in contrast to an almost Gaussian distribution of conductances in adisordered metallic sample connected to a reservoir by broad multi-channelleads. In the absence of time-reversal symmetry, our results obtained withinthe diagrammatic approach coincide with those derived within non-perturbativetechniques. In addition, we show that the distribution has lognormal tails forweak disorder, similar to the case of broad leads, and that it becomes almostlognormal as the amount of disorder is increased towards the Andersontransition.Comment: 14 pages in the ReVTeX preprint format, including 5 postscript  figures; to be published in J.Phys.:Cond.Mat., 199

Mesoscopic conductance fluctuations in dirty quantum dots with single channel leads