FIRSTANSWER: TANK G  (Wrong – see green below.)

REASONING:

As A begins to fill, it will almost immediately begin to flow into B (before rising higher).  As B begins to fill, it will likewise flow into C.  As C fills (and before it gets to the J outlet), it will begin to flow into D. As the water comes into D, it will run directly into G, and continue until G is filled. (Note that water cannot get into E until D is almost full.)

BUT WAIT!!  Looking closer, the outlet from C to D is apparently blocked!!   (How tricky!) SO, . . 

SECOND ANSWER: TANK F

REASONING: (We can use the same first two sentences as above.)

As A begins to fill, it will almost immediately begin to flow into B (before rising higher).  As B begins to fill, it will likewise flow into C. Since the outlet to D is blocked, the water will rise in C until it begins to spill into J.  As the water rises in J, it will first enter the outlet into I, but water in that outlet will only rise as fast as the water in J. As the water in J reaches the outlet to L, it will begin to flow into that tank (L). The water in L will immediately begin to empty into the outlet below, which goes toward H and F.  But since the outlet into H is BLOCKED (!) will begin to rise in F, and will fill F completely (first tank to fill) just before the water in L retreats into J (and eventually I and K).