We present the relation between stellar specific angular momentum $j_*$, stellar mass $M_*$, and bulge-to-total light ratio $beta$ for THINGS, CALIFA and Romanowsky & Fall datasets, exploring the existence of a fundamental plane between these parameters as first suggested by Obreschkow & Glazebrook. Our best-fit $M_*-j_*$ relation yields a slope of $alpha = 1.03 pm 0.11$ with a trivariate fit including $beta$. When ignoring the effect of $beta$, the exponent $alpha = 0.56 pm 0.06$ is consistent with $alpha = 2/3$ predicted for dark matter halos. There is a linear $beta - j_*/M_*$ relation for $beta lesssim 0.4$, exhibiting a general trend of increasing $beta$ with decreasing $j_*/M_*$. Galaxies with $beta gtrsim 0.4$ have higher $j_*$ than predicted by the relation. Pseudobulge galaxies have preferentially lower $beta$ for a given $j_*/M_*$ than galaxies that contain classical bulges. Pseudobulge galaxies follow a well-defined track in $beta - j_*/M_*$ space, consistent with Obreschkow & Glazebrook, while galaxies with classical bulges do not. These results are consistent with the hypothesis that while growth in either bulge type is linked to a decrease in $j_*/M_*$, the mechanisms that build pseudobulges seem to be less efficient at increasing bulge mass per decrease in specific angular momentum than those that build classical bulges.
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