I own a home in 1 state & move to another state, but continue to pay for my home, do I deduct the mort. interest in the old state only or allocate it across both states?

It depends on the states in question; however, you likely will not have to allocate the mortgage interest itself.  Start by entering all of your eligible itemized deductions into the system for your Federal Return, because your Federal Return does not differentiate between which states you paid mortgage interest, but rather, that you did pay mortgage interest and are qualified to deduct the interest.

Not all states allow for itemizing deductions, but many that do prorate the deductions, not by how much interest and other deductions you had while living in the state, but rather by percentage of income in the state.  In other words, they use all of your income and all of your deductions (by their state law) to determine how much tax you would pay in that state.  Then they prorate the final result to the percentage of income you earned in that state.  

The reason is for simplification:  so that you don't have to go through and determine how much interest goes to one state verses the other state, and so forth.  

The one caveat is if the state return in question specifically asks for the allocation amount of interest.  If that is the case, then allocate the interest you paid on the property in that state for that state return.  Chances are, however, that it will not be necessary.