How have appellate courts dealt with challenges to the sufficiency of the evidence to support the finding of a finding of fact?

Any challenge to the sufficiency of the evidence to support the finding of a trial judge is met at the outset with an often repeated sentence, which may be quoted again, with emphasis slightly changed from the 'begins and ends' part (so frequently italicized) to the word 'power': When a finding of fact is attacked on the ground that there is not any substantial evidence to sustain it, the power of an appellate court begins and ends with the determination as to whether there is any substantial evidence, contradicted or uncontradicted, which will support the finding of fact. (Grainger v. Antoyan, 48 Cal.2d 805, 807, 313 P.2d 848.) So, what is spoken of is the very authority of an appellate court.