Photometric observations of 12 totally eclipsing W UMa binaries (NSVS 3325547, V646 Lac, V1320 Cas, V539 Dra, V816 Cep, NSVS 9045055, V1115 Cas, V902 Cep, V596 Peg, NSVS 1768818, V619 Peg, and NSVS 3198272) are presented. We found that the longer (in phase units) the flat eclipses are, the smaller the mass ratios (or the reciprocal values) are. The mass ratios of five targets turned out close to the lower-mass ratio limit. We found that the periods of V1115 Cas and V646 Lac increase, while that of V596 Peg decreases. Masses, radii, and luminosities of the target components were calculated by the light-curve solutions and Gaia distances. In order to perform more reliable statistical analysis of the results we added to the sample of 12 targets from this paper another 29 totally eclipsing W UMa stars studied by us earlier. As a result we found the following trends: (a) the radius and luminosity of the target components increase with their mass but the dependencies are different from those of main-sequence (MS) stars; (b) the temperatures of stellar components whose masses are above 1 M ⊙ tend to be lower than those of the corresponding MS stars, while the temperatures of stellar components whose masses are below 1 M ⊙ tend to be higher than those of the corresponding MS stars; (c) there is no relationship between the fillout factor and mass ratio; and (d) 11 of the 41 targets are of A subtype, 24 are of W subtype, and 6 systems are with equal-temperature components.