  We present a three-dimensional (3D) study of common envelope events (CEEs) to
provide a foundation for future one-dimensional (1D) methods to model the
self-regulated phase of a CEE. The considered CEEs with a low-mass red giant
end with one of three different outcomes -- merger, slow spiral-in, or prompt
formation of a binary. To understand which physical processes determine
different outcomes, and to evaluate how well 1D simulations model the
self-regulated phase of a CEE, we introduce tools that map our 3D models to 1D
profiles. We discuss the differences in the angular momentum and energy
redistribution in 1D and 3D codes. We identified four types of ejection
processes: the pre-plunge-in ejection, the outflow during the plunge-in, the
outflow driven by recombination, and the ejection triggered by a contraction of
the circumbinary envelope. Significant mass is lost in all cases, including the
mergers. Therefore a self-regulated spiral-in can start only with a strongly
reduced envelope mass. We derive the condition to start a recombination
outflow, which can proceed either as a runaway or a stationary outflow. We show
that the way the energy of the inspiraling companion is added to the envelope
in 1D studies intensifies the envelope's entropy increase, alters the start of
the recombination outflow, and leads to different outcomes in 1D and 3D
studies. The steady recombination outflow may dispel most of the envelope in
all slow spiral-in cases, making the existence of a long-term self-regulated
phase debatable, at least for low-mass giant donors.
