Question: I would like your advice about what I should bid in the following situation. Partner opens 1C, I answer 1H, he bids 2H. My hand is:

S : none  

H : K Q J x x x  

D : A K Q x x x  

C : J 

What should I bid now?

Answer: 
There is a convention called "exclusion blackwood" (some call it "voidwood"). This way you can ask for aces, excluding one suit.

This call can be made by bidding your void suit, in a level above your fit suit, provided that a fit has been found.

In your example, all bids (4s,5c,5d) are exclusion blackwood.

Partner can respond in steps, just like steps on 4NT(depends whether you play standard, blackwood, 1430RKCB, 3014RKCB etc). No matter what kind of blackwood you play, you will get your desired info (this is the two round aces).

You can look [here](http://www.bridgeguys.com/Conventions/exclusion_keycard_blackwood.html) for a variation of exclusion blackwood.
From my comment to Thanos' answer:

Logically speaking, 3S splinter followed by 4NT over the expected 4H by partner should be keycard ask, without counting the Spade Ace (otherwise why not bid 4NT directly?). If partner bids 4D (likely singleton), you can still continue with a 4S bid and partner will know to take you further with the heart or club Ace.

So I would suggest bidding 3S, followed by 4NT over 4H.