It is certainly possessive. I learned that 之 is a classical way to say 的, making it a possessive particle.

An example sentence would be 父母之爱 

However I've seen examples like 

自知之明, which to me indicates it is attributive?


ALSO from my understanding it is mostly written, not spoken.  


P.S.

I understand possessive to mean that an object "own's"  a characteristic or another object. e.g. 我的肚子 (it's MY stomach). 

I understand "attributive" to mean that a quality ( e.g.快）is associated with the object or subject (e.g. 兔子） ＝ 快的兔子。 ( in this example the quality fast, is attributed to the rabbit) 


Hahaha, hope that helps. Not sure about 其 or 彼.... :S

Sources:

1.我聪明之老师 (杨老师） 
2. http://www.yellowbridge.com/chinese/dictionary.php?word=之
3. http://www.linedict.com/dict.html#/cnen/entry/c56e6059137441a99d708c56ab0515d1