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We present Monte Carlo calculations of Lyman alpha (Lya) radiative transfer through collapsing gas clouds, representing proto-galaxies that are caught in the process of their assembly. Such galaxies produce Lya flux over an extended solid angle from a spatially extended Lya emissivity and/or from scattering effects. We study the effect of the gas distribution and kinematics, and of the Lya emissivity profile, on the emergent spectrum and surface brightness distribution. The emergent Lya spectrum is typically double-peaked and asymmetric. In practice, the blue peak is significantly enhanced and the red peak, in most cases, will be undetectable. The resulting effective blueshift, combined with scattering in the intergalactic medium, will render extended Lya emission from collapsing protogalaxies difficult to detect beyond redshift z=4. The surface brightness distribution is typically flat, and a strong wavelength dependence of its slope (with preferential flattening at the red side of the line) would be a robust indication that Lya photons are being generated (rather than just scattered) in a spatially extended region around the galaxy. We also find that for self-ionized clouds whose effective Lya optical depth is less than 10^3, infall and outflow models can produce nearly identical spectra and surface brightness distributions, and are difficult to distinguish from one another. The presence of deuterium with a cosmic abundance may produce a narrow but detectable dip in the spectra of systems with moderate hydrogen column densities, in the range 10^18-10^20 cm^-2. Finally, we present a new analytic solution for the emerging Lya spectrum in the limiting case of a static uniform sphere, extending previous solutions for static plane-parallel slabs.