WI:Henry I explicity appointed Henry Curtmantle as his heir instead of Matilda?

Just a thought,what if after Henry Curtmantle(future Henry II) was born,his grandfather explicitly appointed him as his heir rather than his mother?Would the anarchy still break out when Henry I dies?
 
Some barons will probably try it on. Depends if the Regent (Robert of Gloucester?) stomps on the first one who makes a move.
 
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