My first answer would be : 1 solar system. While any race could potentially spread across an enire galaxy, jumping beyond your own galaxy are just TO long distances to be plausible. There are plenty stars within 10 lightyears that are totally at reach within normal science boundries. And one could just start a colony there and launch from theire beyond.. slowly spreading out over the whole galaxy. But the long distanced between stars would make having a central center of goverment impractical, so it would heavy rely on local rules and local legions/fleets to govern those colony's, and send home the gains to the imperial home-planet. Whith such long lines, I expect every planet to declare independance from the empire, and the empire being unable to do anything about it. as such the race would be spread out in the whole galaxy.. but it would not be 1 empire, but rather hundreds of thousands of them each existing of the planets within 1 solar-system. some might be at war with eachother, some may trade with eachother.. some may try to form some form of federation of independant empires.
So in short a SPACE empire could just never exist.. every trip would be a single trip.
first you would need energy. Since the energy needs need to be reasonable... (zero point energy is out of the question as is warp travel) also you cannot surpass 5c, or your crew would be tomato soup. I also presume that the ship is magneticly shielded, so hard radiation nor tiny space particles would be a problem (you bend them around you, as the impact of even 1 atom at 0.5c on your ship would be imposible to armor plate agains)
So I would think you exelerated constantly at a maximum of 5g for 6 months, towards 0.5c (before the energy needs outstrip the usefullness of going faster) than fly in 7.5 more years to the nearest starm and than start decelerating for 6 months. This way you'd made the trip in 8 years. *if you were to turn around and return you would have flown for 16 years, yet almost 19 would have passed on your home planet.
thats doable. 947
However even if you were to communicate with your home planet.. 4 years to get a reply is just TOO long to be of any use for any empire. (the roman empire collapsed and it had 2 WEEKS communication lines) and the roman empire also gave strong power to local leaders.. with local legions, and the imperial army being slow to responce if needed if regional leaders rebelled against rome.
in this situation.. any news about any rebellion would take 4 years to arive.. and responsive action would take 13 years to arrive. it would pretty hard to keep onder in that kind of a situation. And thats why I presume that no empire as such could excist.
But supposing that all colony's are loyal to the home world (their not like humans that like to self govern, but LOVE to please their empire-king or something like that) that it comes down to travel time towards the center of the empire. Are there any ouside attacks? than no space empire of such could excist as responding would just take to long.. you would have lost the battle decades before you could send a counterattack. But suppose you got none of that to?
Than it bottles down to lifespan or energy. every 1 lightyears of distance, means 2.25 years of flight. it takes for humans at least 25 years to be properly trained, and they can reach 120 years (when we reach our biological optimum) If you were to swap them for new crew for the return flight.. this would give us close to 100 years of flight enough to cross 50 lightyears (giving us the maximum size for a human space empire) However biological immotality is theoretical possible.. and while it could take halve a million year to fly across some galaxy's even at 0.5c, if one does not age or the ship is generational, it is plausible.
But energy, even a ship that could continue flying, would need to refuel, at the very least to be able to maintain life-support and keep growing food. (even biodomes need HEAT, as space is cold and perfect isolation does not excist) also the magnetic shielding and artificial gravity would consume energy) * there are 2 methods to aquire this extra fuel (A) bring it all along, meaning more fuelload, giving every less return on cargo. or.. *refuel at a colony every 4-10 lightyears, jumping towards the home planet in steps (having the disadvantage o having to decellerate/acellerate more often, increasing travel times and fuel use.
But suppose they would just DROP the cargo at the second base, and return.. 947