And if I understand correctly, in order to get KING or ROBBER BARON card, one need to build (it means to OWN) city or road that has more tiles in it that previous one. Am I correct?
The king or robber baron tile is awarded to the player who
completes a
longer road or a
larger city. The player completing the longer feature does
not have to own the feature concerned.
For example, a player is awarded the king tile when he completes a 2 tiled city. I then close a city containing 5 tiles. The king tile is then passed to me. Another player might also then complete a 5 tiled city. The king tile is
not shared, it remains with me. However, if someone completes a 6 tiled city, then the king tile is passed to that player. This is the same for the robber baron tile for road building. The road being completed must be
longer than the previous longest road and
not equal to for the robber baron tile to be passed on.
At game end, the player holding the king tile recieves 1 point per completed city and the holder of the robber baron tile recieves 1 point per completed road (This, as you rightly said, is regardless of who owns the road or cities and who completed them).
It is helpful to keep track of the size of the city/road on the scoreboard by using neutral coloured tokens, etc. In my case I use a purple coloured meeple (purple=king) to indicate the size of the largest city so far, and a brown coloured meeple (brown=robber) to indicate the size of the largest road so far.