Mysql – How to update a column in a table with data from another, unrelated tables columns data jus in order it selected

The proper form would be (assuming current pg version 9.3 for lack of information):

UPDATE C 
SET    column1 = A.column1 
     , column2 = B.column2 
     , column3 = A.column1 + B.column2
FROM   A
JOIN   B ON A.id = B.id  -- ??? not specified in question!
WHERE  C.id = A.id      --  ??? not specified in question!
AND   (C.column1, C.column2, C.column3) IS DISTINCT FROM
      (A.column1, B.column2, A.column1 + B.column2);

The last WHERE clause is optional to avoid empty updates that would not change anything (but still write a new row version at full cost).

ypercube already gave a basic explanation in his comment:

You don't get duplication. Your derived table is cross joining A and B (i.e. without any joining condition) and then choosing an arbitrary row (LIMIT 1 without ORDER BY). It then uses the values from that arbitrary row to update all rows of table C. If you want different values to be used for different rows of C, you'll have to join the 3 tables (using JOIN - ON and WHERE)

Refer to the manual on UPDATE for details.

This works - I had the JOIN wrong

UPDATE `events` 
  INNER JOIN `plays_in_events` ON (`plays_in_events`.`EventID` = `events`.`EventID`)
  INNER JOIN `plays` ON (`plays_in_events`.`PlayID` = `plays`.`PlayID`)
  SET events.Name = plays.Play
WHERE 
  events.Name IS NULL and plays_in_events.PlayID = 1

and the earlier comments were quite right, but it took me a while to 'get it' - thanks for your help. I had just copied the JOIN lines from the working SELECT query, but when I looked again, I could finally see what the commentators meant about events appearing twice, and plays_in_events not appearing properly in the JOINs.