Two thoughts: One, the answers show that people answering questions out of their area do not take into account local customs. Arizona does not use attorneys for residential real estate transactions, so ignore those comments.
Two, why would one pay cash when there is five-year money to be had for less than 3% (with an even lower effective rate if you factor in the tax deductions)? I would think if you have enough money to pay cash for a home, then you have enough money to be working with a financial advisor who could help you get a higher rate of return on those funds fairly easily...Just a thought.
For closing costs, you should exepct to pay an attorney or Titile company, recording fees, title insurance, homewoenrs insurance, if there's land with the property you should have a survey done, and even though your paying in cash, I would strongly advise you to have an appraisal done. Finally there are things such as home inspections, well and septic inspections if necessary, and insect inspections if necessary in your area. I don't know what the going rates are in AZ, but I've worked in more than one location over the years and without know the size of the house or lot, I'd suggest that you're looking at spending another couple of $2500+/- to handle the above.
Good Luck and Happy House Hunting.