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The question of the existence of active tidal disruption around various dSphgalaxies remains controversial. That debate often centers on the nature (boundvs. unbound) of extended populations of stars. However, the more fundamentalissue of the very existence of the extended populations is still contentious.We present an evaluation of the debate centering on one particular dSph,Carina, for which claims both for and against the existence of stars beyond theKing radius have been made. Our review includes an examination of all previousstudies bearing on the Carina radial profile and shows that the survey methodwhich achieves the highest detected dSph signal-to-background in the outerparts of the galaxy is the Washington M, T2 + DDO51 (MTD) filter approach fromPaper II in this series. We then address statistical methods used to evaluatethe reliability of MTD surveys in the presence of photometric errors and forwhich a new, a posteriori statistical analysis methodology is provided.Finally, these statistical methods are tested by new spectroscopy of stars inthe MTD-selected Carina candidate sample. Of 74 candidate giants with follow-upspectroscopy, the MTD technique identified 61 new Carina members, including 8stars outside the King radius. From a sample of 29 stars not initiallyidentified as candidate Carina giants but that lie just outside of ourselection criteria, 12 have radial velocities consistent with membership,including 5 extratidal stars. Carina is shown to have an extended population ofgiant stars extending to a major axis radius of 40' (1.44x the nominal Kingradius).Comment: 56 pages, 10 figures. Submitted to the Astronomical Journal, 2004 Sep  2

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Exploring Halo Substructure with Giant Stars. VI. Extended Distributions of Giant Stars around the Carina Dwarf Spheroidal Galaxy: How Reliable Are They?