No, unless an ability specifically mentions counters of some sort, there are no counters involved.
May 27, 2014 10:21 a.m.
Counters only get placed on creatures when it specifically says so. You might see people put them on creatures like Bloodthrone Vampire as a reminder but this is bad practice.
May 27, 2014 10:38 a.m.
To expand on the above answer, there are two kinds of buffs in Magic.
First, there are static buffs, which grant P/T changes for a duration. Some effects wear off at end of turn (usually those granted by activated or triggered abilities or by spells). Some effects last indefinitely (usually those granted by static abilities of permanents).
Second, there are counters, which are usually used to visually mark indefinite changes in P/T from non-static sources. Effects only uses counters if they specify that they do.
Bloodthrone Vampire 's ability doesn't mention counters, so it's just a static effect.