Kardashev 2 Worldship
In 1987 Burruss & Colwell proposed such an advanced worldship concept.
* 1,000 kilometer wide World-Ship
* 50 billion passengers
* cruise speed of 0.4c (40% of lightspeed).
* The antimatter fuel required would be the equivalent of several days worth of the Sun’s total luminosity, so it would require at least a Kardashev Type II Civilization dedicated to the task to achieve it.
Kardashev 3 sending planets via blackhole gravity slightshot
A Type III Civilization, with control over the Galaxy’s resources, could fling Intergalactic Planet-Ships outwards at 0.5c (50% of lightspeed). But what would it require to stop in the target Galaxy?
Given the right materials a magnetic-sail might do the job. We can slow an Earth-Ship from 0.5c to 0.005c in about 550,000 years (11% of the trip-time) over a braking distance of about 36,000 light-years.
The magnetic sail would be 13.4 AU in radius with a super-current of 68 giga-amps and a mass of about 15.4 quadrillion tonnes (if its density is about that of carbon nanotubes.) Thus immensely BIG and probably immensely strong. At the “wire” (1.5 metres in radius) the field strength is 9,240 tesla, which is about 100 times higher than the highest critical magnetic field strength of known super-conductors. Thus not material we presently possess.