Repair Ships

You can use the this phase to repair a damaged ship beyond what it can auto-repair on its own.  You can repair two DP for each RU spent, but you can never repair a ship beyond its original DP rating.   A repaired ship's operational rating is correspondingly increased by these repairs.  You cannot repair ships that belong to another empire unless you are formally allied with that empire.
Damaged ships can be repaired in any sector, but you must specify which world will supply the RU for the repairs.  You may schedule contingency repair orders for ships which you expect will be damaged during the upcoming turn, but if that ship is not damaged (or if it is destroyed) then no repairs will be performed, and the RU earmarked for those repairs will sit idle.  A world cannot fund a repair operation on the same turn that you take possession of it.  Note that repairs are always visible to any empire which has an unloaded ship in the same sector.
If a world is blockaded (but not interdicted), then ships belonging to that world's owner can still be repaired in that world's sector, but the RU on that world can be used to fund repairs only on that world.  That is, since the blockade prevents RU from being shipped off-world, they cannot be used to fund repairs elsewhere; however, the lack of interdiction does not prohibit repairs at that world itself.
If a world is interdicted (and therefore also blockaded), then no ship belonging to that world's owner (or an ally) can be repaired in that world's sector (regardless of where the RU funds come from), and RU at that world cannot be used to fund repairs anywhere at all.  That is, the interdiction prohibits that world's owner from conducting repairs at that world, and the implied blockade prohibits that world's RU from being shipped off-world for repairs.
You can repair a friendly or allied orbital at a ratio of three DP (instead of the normal two) for each RU spent.  In additional orbitals automatically repair fully any friendly or allied ship loaded within it (regardless of any interdiction present in the same sector).
Note that the empires enforcing a blockade or interdiction can repair their ships at the site of the blockade or interdiction so long as the requisite RU are available from some other (unblockaded) world.  Repairs can always be performed in empty space sectors that do not contain worlds, regardless of the empires present.
Allies: Allied empires can repair each other's ships for normal RU cost.
Abandoned Empire: Any RUs which cannot be spent on building new ships will be used to repair damaged ships, starting with the ship that has the smallest operational rating (or fewest remaining DP if there's a tie).