How is "becoming" (bhava) defined in the context of Dependent
There are three types of "becoming" (bhava) defined in the context of Dependent Co-arising, namely, sensual, form & formless becoming. For example, when it is read on forums: "I have attained jhana", this is an example of "form becoming".
Attachment is the condition for becoming. Attachment includes the view or theory of "self" (attavādupādānaṃ).
If there is craving, will that craving always result in "becoming"?
Craving does not always result in becoming. Note: Craving does not include thinking of "I". Craving is merely an urge, such as the mind drawn towards an attractive object. Merely the mind drawn towards or attracted to an object is craving.
For example, when the energy of lust runs through the physical body causing a sexual organ to become erect or aroused, this "energy" is not thinking or ego. It is an "energy" or "urge".
Or for example, when the mind says: "Don't eat this food" but the body keeps having the urge to reach out & grab that food, that urge is craving.
It is important to separate "craving" from "thinking" & "selfing" ("becoming") in experience. This should not be too difficult. Simply make the resolution to not eat chocolate, pizza or some unhealthy food you habitually crave. Then notice when you see that food how the craving pushes, pulls & torments the mind; even when the mind or 'self' says "No" to those foods.
Is there something like craving without "becoming"?
Craving without becoming exists although is relatively very rare. Any non-Arahant can experience craving without becoming. For example, any hungry stream-enterer knows when they mindfully eat tasty food, non-verbal craving is subtly arising, which they practise to minimize or pacify. A stream-enterer practising diligently in a monastic setting (eating one or at most two meals per day) easily knows the arising of craving without becoming.