Anagrab is a word game which is usually played with Scrabble tiles. The name is a portmanteau of the words 'anagram' (the basic game mechanism) and 'grab' - because a player's words may at any time be 'grabbed' by opponents. The game was first described in 1976 in Richard Sharp's The Best Games People Play , but his description suggests that he did not invent it.
Letter tiles are placed face down and turned over one at a time. At any point (there are no turns) any player may call out a word of at least four letters. This word can be made either entirely from the pool of letters, or by adding at least one new letter to an existing word. If the new word is acceptable the person who said the word first takes the letters and places them in front of him or her. When making a new word the root of the existing word must be changed - for example you may not add a D to the word LIVE to make LIVED. All the letters in an existing word must be included in the new one, plus at least one more.
When a new letter is turned over, the first person to say a valid word takes it. If more than one is said at the same time the longer word takes it. If the two are the same length (or the same word) then that word(s) are banned for the rest of the game and nobody takes it.
Sharp suggests that the score for each word is the face value of the tiles multiplied by the number of letters in that word. In practice any reasonable system, such as totaling the number of letters held, is acceptable.