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In this instance, the term "worlds" denotes all categories of existence both in the physical and the spiritual sense. The Arabic expression rabb - rendered by me as "Sustainer" - embraces a wide complex of meanings not easily expressed by a single term in another language. It comprises the ideas of having a just claim to the possession of anything and, consequently, authority over it, as well as of rearing, sustaining and fostering anything from its inception to its final completion. Thus, the head of a family is called rabb ad-dar ("master of the house") because he has authority over it and is responsible for its maintenance; similarly, his wife is called rabbat ad-dar ("mistress of the house"). Preceded by the definite article al, the designation rabb is applied, in the Qur'an, exclusively to God as the sole fosterer and sustainer of all creation - objective as well as conceptual - and therefore the ultimate source of all authority.
i.e., Lord of everything in existence including angels, humans, and animals.
The Arabic word Rabb, usually translated Lord, has also the meaning of cherishing, sustaining, bringing to maturity. God cares for all the worlds He has created.