Is it correct that dependent origination will cease to exist if one doesn't have 12 nidanas? From Pratītyasamutpāda - Wikipedia:


  dependent origination refers to nothing else but the process of mental conditioning as described by the twelve nidanas


So to check if my understanding is correct, will dependent origination cease to exist if one doesn't have 12 nidanas? 

In my understanding, dependant origination is just an extended understanding of "condition". For example, if I say "plants need water, soil and light to grow", then water, soil and light are the originations. This doesn't seem to relate to the mental condition of the observer. So how do the two relate? 

And in general, how does one know that all dependent originations of a thing are "depleted"?
will dependent origination cease to exist if one doesn't have 12 nidanas?


Yes. 


  In my understanding, dependant origination is just an extended understanding of "condition". For example, if I say "plants need
  water, soil and light to grow", then water, soil and light are the
  originations. This doesn't seem to relate to the mental condition of
  the observer. So how do the two relate?


'Paticcasumuppada' ('Dependent Co-Arising') is the subset of 'Idappaccayatā' ('Conditionality') that explains the 12 conditions for the arising of mental suffering. The suttas say: 


  And what is dependent co-arising? From ignorance as a requisite condition come fabrications. From fabrications as a requisite
  condition comes consciousness. From consciousness as a requisite
  condition comes name-&amp;-form. From name-&amp;-form as a requisite condition
  come the six sense media. From the six sense media as a requisite
  condition comes contact. From contact as a requisite condition comes
  feeling. From feeling as a requisite condition comes craving. From
  craving as a requisite condition comes clinging. From
  clinging as a requisite condition comes becoming. From
  becoming as a requisite condition comes birth. From birth as a
  requisite condition, then aging &amp; death, sorrow, lamentation, pain,
  distress, &amp; despair come into play. Such is the origination of this
  entire mass of stress &amp; suffering.


The conditionality related to the arising or coming-to-be of trees is not called 'Paticcasumuppada'. The arising of trees is merely an example of general 'Idappaccayatā'. 


  And in general, how does one know that all dependent originations of a thing are "depleted"?


This question is not valid because not all examples or occurrences of 'Idappaccayatā' are 'Paticcasumuppada'. The mind (while living) can experience the depletion of 'Paticcasumuppada' but the mind (while living) cannot experience the depletion of 'Idappaccayatā'. Even though the suffering of 'Paticcasumuppada' can end; the 'Idappaccayatā' of Nature will continue to be discerned. In short, suffering can end but trees will continue to grow, clouds will continue to form, the body will continue to live nourished by food, consciousness will continue to operate conditioned by sense organs, etc.