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 galaxys 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.
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