  We present an analysis of new and archival ALMA observations of molecular gas
in twelve central cluster galaxies. We examine emerging trends in molecular
filament morphology and gas velocities to understand their origins. Molecular
gas masses in these systems span $10^9-10^{11}\mathrm{M}_{\odot}$, far more
than most gas-rich galaxies. ALMA images reveal a distribution of morphologies
from filamentary to disk-dominated structures. Circumnuclear disks on
kiloparsec scales appear rare. In most systems, half to nearly all of the
molecular gas lies in filamentary structures with masses of a few
$\times10^{8-10}\mathrm{M}_{\odot}$ that extend radially several to several
tens of kpc. In nearly all cases the molecular gas velocities lie far below
stellar velocity dispersions, indicating youth, transience or both. Filament
bulk velocities lie far below the galaxy's escape and free-fall speeds
indicating they are bound and being decelerated. Most extended molecular
filaments surround or lie beneath radio bubbles inflated by the central AGN.
Smooth velocity gradients found along the filaments are consistent with gas
flowing along streamlines surrounding these bubbles. Evidence suggests most of
the molecular clouds formed from low entropy X-ray gas that became thermally
unstable and cooled when lifted by the buoyant bubbles. Uplifted gas will stall
and fall back to the galaxy in a circulating flow. The distribution in
morphologies from filament to disk-dominated sources therefore implies slowly
evolving molecular structures driven by the episodic activity of the AGN.
