If you have any kind of artifitial gravity, it would most likely be shielded off ouside your ship.
If it wasnt, asteroids would fall on your ship very quickly if they passed near them, and so would other ships, no matter their size (even battleships).
Gravity decreases with the second power of distance (well at least in our normal universe where artifitial gravity is actually impossible), and thats a constant.
That means that an object 1 mile above your ship would fall onto your ship at the same rate that the object would fall upon the earth 1 mile above sea level, if your ship's artifitial gravity is also 9.81 m/s^2.
That's pretty painfull if its a medium sized asteroid or other ship.
So, its probably shielded off at the edges.
In Star Trek DS9, there is an episode where captain Ciskko and his son fly to Cardasia in a primitive "solar sail ship". In that episode the artifitial gravity is explained: They use a "gravity rug" on the floor.