You have to pay a DEWA (Dubai Electricity & Water Authority) deposit, which IIRC is AED 1,000 for an apartment and AED 2,000 for a villa.

Your DEWA bill for a 3 bed apartment should be well under AED 400 a month.

If you are after a landline, I really don't now about deposits (you buy your own handsets), but you should be able to find the costs at either of the providers websites - Etisalat or Du.

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