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Propagating The Last Non-Null Value With T-SQL

Tomaz Kastrun shows a great use of window functions in T-SQL:

So you have NULL values in your SQL Server table and you want to populate those NULL values with the last non-NULL value, based on a particular order. Once you have only one NULL values encapsulated between two populated values, there are quick and fast solutions. But what if you find a larger gap of NULL values and you want to populate these values as well?

Click through for a partial solution, followed by the real solution.