The morphology and molecular conformation of Langmuir-Blodgett deposited and floating monolayers of a selection of straight chain (eicosanoic acid, EA), iso (19-methyl eicosanoic acid, 19-MEA), and anteiso (18-methyl eicosanoic acid, 18-MEA) fatty acids have been investigated by Vibrational Sum Frequency Spectroscopy (VSFS), AFM imaging, and the Langmuir trough. While the straight chain fatty acid forms smooth, featureless monolayers, all the branched chain fatty acids display 10-50 nm sized domains (larger for 19-MEA than the 18-MEA) with a homogeneous size distribution. A model is suggested to explain the domain formation and size in terms of the branched fatty acid packing properties and the formation of hemispherical caps at the liquid-air interface. No difference between the chiral (S) form and the racemic mixture of the 18-MEA is observed with any of the utilized techniques. The aliphatic chains of the straight chain fatty acids appear to be oriented perpendicular to the sample surface, based on an orientational analysis of VSFS data and the odd/even effect. In addition, the selection of the subphase (neat water or CdCl2 containing water buffered to pH 6.0) used for the LB-deposition has a profound influence on the monolayer morphology, packing density, compressibility, and conformational order. Finally, the orientation of the 19-MEA dimethyl moiety is estimated, and a strategy for performing an orientational analysis to determine the complete molecular orientation of the aliphatic chains of 19-MEA and 18-MEA is outlined and discussed.