This might be quite basic. I am just a beginner and searched through the web and the rule book and couldn't find the answer.
For instance, Ajani's Pridemate lets you,
Whenever you gain life, you may put a +1/+1 counter on Ajani's Pridemate. (For example, if an effect causes you to gain 3 life, you may put one +1/+1 counter on this creature.)
Then does that counter(s) last across turns and accumulate making Ajani's Pridemate much stronger creature as the game progresses until it dies? Say, you have a staff that lets you
Whenever you cast a black spell or a Swamp enters the battlefield under your control, you gain 1 life.
Every turn you put down a Swamp you gain 1 life and hence Ajani's Pridemate gets another +1/+1 counter. It can even become like 2/2 + 1000*(+1/+1 counter) making it 1002/1002. Am I right?