The clue when filled in goes from top row to the bottom row of the grid, & I suppose 'absolutely' could be the expression 'from top to bottom' but I don't like it. Maybe someone else can explain better.
I think you're right mercedita but it's a bit of a dodgy clue, not least because you can't qualify 'unique' with 'absolutely' (or anything else for that matter))
I take your point pixie. If "Absolutely" is the definition and "unique as this grid entry" is the wordplay then it works cryptically but the surface reading is still ungrammatical.
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Sunday Times Prize Crossword 4578 Sunday February 23Rd 2014