  Accreting supermassive black holes (SMBHs) produce highly magnetized
relativistic jets that tend to collimate gradually as they propagate outward.
However, recent radio interferometric observations of the 3C 84 galaxy reveal a
stunning, cylindrical jet already at several hundred SMBH gravitational radii,
$r\gtrsim350r_{\rm g}$. We explore how such extreme collimation emerges via a
suite of 3D general-relativistic magnetohydrodynamic (GRMHD) simulations. We
consider an SMBH surrounded by a magnetized torus immersed in a
constant-density ambient medium that starts at the edge of the SMBH sphere of
influence, chosen to be much larger than the SMBH gravitational radius,
$r_{\text{B}}=10^3r_{\text{g}}$. We find that radiatively inefficient accretion
flows (e.g., M87) produce winds that collimate the jets into parabolas near the
BH. After the disk winds stop collimating the jets at $r\lesssim{}r_\text{B}$,
they turn conical. Once outside $r_\text{B}$, the jets run into the ambient
medium and form backflows that collimate the jets into cylinders some distance
beyond $r_{\text{B}}$. Interestingly, for radiatively-efficient accretion, as
in 3C 84, the radiative cooling saps the energy out of the disk winds: at early
times, they cannot efficiently collimate the jets, which skip the initial
parabolic collimation stage, start out conical near the SMBH, and turn into
cylinders already at $r\simeq300r_{\rm g}$, as observed in 3C 84. Over time,
jet power remains approximately constant, whereas the mass accretion rate
increases: the winds grow in strength and start to collimate the jets, which
become quasi-parabolic near the base; the transition point to a nearly
cylindrical jet profile moves outward while remaining inside $r_\text{B}$.
