A few questions about "becoming" How is "becoming" (bhava) defined in the context of Dependent Co-arising?

If there is craving, will that craving always result in "becoming"?

Is there something like craving without "becoming"?

Thanks for your time and patience!

EDIT: as I made the mistake of asking more than one question in the same post, I have two different answer (1231546 and Dhammadhatu's) which dissipated my doubts. 

Thanks!
How is "becoming" (bhava) defined in the context of Dependent Co-arising?


it is explained as formation of various existence in the three ranges of existence;


  AN 3.76  Bhava Sutta: Becoming (1)
  
  Then Ven. Ananda went to the Blessed One and, on arrival, bowed down
  to him and sat to one side. As he was sitting there he said to the
  Blessed One, "Lord, this word, 'becoming, becoming' — to what extent
  is there becoming?"[1]
  
  "Ananda, if there were no kamma ripening in the sensuality-property,
  would sensuality-becoming be discerned?"
  
  "No, lord."
  
  "Thus kamma is the field, consciousness the seed, and craving the
  moisture.[2] The consciousness of living beings hindered by ignorance
  &amp; fettered by craving is established in/tuned to a lower property.
  Thus there is the production of renewed becoming in the future.
  
  "If there were no kamma ripening in the form-property, would
  form-becoming be discerned?"
  
  "No, lord."
  
  "Thus kamma is the field, consciousness the seed, and craving the
  moisture. The consciousness of living beings hindered by ignorance &amp;
  fettered by craving is established in/tuned to a middling property.
  Thus there is the production of renewed becoming in the future.
  
  "If there were no kamma ripening in the formless-property, would
  formless-becoming be discerned?"
  
  "No, lord."
  
  "Thus kamma is the field, consciousness the seed, and craving the
  moisture. The consciousness of living beings hindered by ignorance &amp;
  fettered by craving is established in/tuned to a refined property.
  Thus there is the production of renewed becoming in the future. This
  is how there is becoming."
  https://www.accesstoinsight.org/tipitaka/an/an03/an03.076.than.html



If there is craving, will that craving always result in "becoming"?


Yes craving is always for a state with certain conditions or a state without certain conditions, either way craving for something dependent on conditions becoming like this or otherwise, becoming better or worse, good or bad etc.

If one talks about craving for the cessation of craving, such craving can be explained as being dispersive of becoming to the extent that it is for abandoning of craving and therefore becoming but still it is craving for a conditioned state, a state without certain conditions, without craving. There is nothing further after that and craving is at that point uprooted due to complete disenchantment.


  Then Ven. Ananda approached the nun and, on arrival, sat down on a
  prepared seat. As he was sitting there, he said to the nun: "This
  body, sister, comes into being through food. And yet it is by relying
  on food that food is to be abandoned.
  
  "This body comes into being through craving. And yet it is by relying
  on craving that craving is to be abandoned.https://www.accesstoinsight.org/tipitaka/an/an04/an04.159.than.html



Is there something like craving without "becoming"?


i am not sure what you mean.