Here are three hits for Maricopa County programs to give away free shade trees to homeowners. I have checked them only a little and am just passing it along.

SRP Shade Tree Program in Arizona is providing up to 2
desert adapted trees (Palo Verde, Thornless Palo Verde, Native Mesquite, Thornless Mesquite, Desert Willow, Willow Acacia) for homes built before 1980 & up to 2 for all other
homes. You must meet their qualifications & attend a SRP Shade Tree
Workshop to get your trees, which come in 5 gal containers, up to 6’ in
height. You must be a homeowner of a single family residence to qualify. http://www.savewithsrp.com/RD/shadetreeworkshops.aspx

About Energy-Saving Trees: Energy-Saving Trees is a
research-based tool intended to help homeowners and utility companies save
energy and money by strategically planting trees. http://energysavingtrees.arborday.org/?partnerCode=07010#Home

APS is offering residents the chance to get FREE Shade Trees
as part of their Shade Tree Program in Phoenix. To receive free trees you must
complete a tree care workshop online or in person. Register for an
instructor led workshop at https://www.aps.com/en/residential/savemoneyandenergy/homeappliance/Pages/shade-tree-program.aspx or by calling 602-357-0032. (Warning: web site is wonky).