Bioshift: move any number of +1/+1 counters from target creature onto another creature with the same controller.
Branching evolution: if one of more +1/+1 counters would be put on a creature you control, twice that many +1/+1counters are put on that creature instead.
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-MadMage
For purposes of Branching Evolution, "mov[ing]" counters from one creature onto another includes "put[ting]" those counters onto the latter creature (C.R. 122.5), so that Branching Evolution would double the number of +1/+1 counters put on the latter creature this way.
In general, a counter is "put" on a permanent if the effect says "put ... counter[s]", "move ... counter[s]" (C.R. 122.5), "double the number of ... counter[s]" (C.R. 701.9e), or "enter[s]" or "put ... onto" or "return ... to" "the battlefield ... with ... counter[s]" (C.R. 122.6). See also this thread and this thread.
Note that Branching Evolution's ability is not a triggered ability (it lacks "when", "whenever", and "at") (C.R. 603.1).
For purposes of Branching Evolution, if you "double the number of +1/+1 counters" on an object, you normally put as many +1/+1 counters on it as it has, so that with Branching Evolution, you put twice that many of those counters instead (C.R. 701.9e). For example, if you control Branching Evolution, Kalonian Hydra has three +1/+1 counters on it, and you "double the number of +1/+1 counters" on it, you put six more +1/+1 counters on it (rather than three) for a total of nine +1/+1 counters.
Note again that Branching Evolution's ability is not a triggered ability, so that ability doesn't "trigger".
As far as the rules are concerned, putting counters on an object includes—
"putting counters on that object while it's on the battlefield", regardless of what verb is used to refer to that action (whether "put", "move" [C.R. 122.5], "double" [C.R. 701.9e], "give", or some other verb), and
the case of "an object that's given counters as it enters the battlefield" (e.g., "enters the battlefield with ... counters")
Bioshift: move any number of +1/+1 counters from target creature onto another creature with the same controller.
Branching evolution: if one of more +1/+1 counters would be put on a creature you control, twice that many +1/+1counters are put on that creature instead.
Using card tags is mandatory in the Magic Rulings forum. Please check your private messages to learn how to use them. I've added them for this post.
-MadMage
> Im sorry about that.
In general, a counter is "put" on a permanent if the effect says "put ... counter[s]", "move ... counter[s]" (C.R. 122.5), "double the number of ... counter[s]" (C.R. 701.9e), or "enter[s]" or "put ... onto" or "return ... to" "the battlefield ... with ... counter[s]" (C.R. 122.6). See also this thread and this thread.
Note that Branching Evolution's ability is not a triggered ability (it lacks "when", "whenever", and "at") (C.R. 603.1).
EDIT: Edited after comment 5 was posted.
Such as kalonian hydra and primordial hydra
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Note again that Branching Evolution's ability is not a triggered ability, so that ability doesn't "trigger".
As far as the rules are concerned, putting counters on an object includes—
To Branching evolution , it is a replacement that say will double the number if i put a +1/+1 counter on a permanent. It cant be countered.