Carrying away can be done by an innocent third person, if say, the item was stashed on them without their knowledge. A common defense in shoplifting occurs when the shoplifter senses they will be stopped, and therefore drops or abandons the item before leaving the store. The element of asportation is settled on the basis of common sense. Under the old common law, only moveable property counted as personal property, but under modern statutes, almost anything qualifies as personal property. The value of the property stolen determines whether the charge is a misdemeanor or felony.
Some states also have particular interests in certain kinds of property.
Evidence rules sometime require experts or appraisers to testify as to the worth of property. Sometimes, as in the case of jewelry, it's difficult for the owner to make an identification. It must also be proven that the owner did not abandon the property, leaving open the honest belief that they did not care if it was taken. Things that are in a wild state, like wildlife, cannot be the property of another. The substantial risk of loss is a fairly new element intended to encompass cases like joyriding, where the thief plans to eventually return the property, but the risk of permanent loss is present.