Wrap systems for medical device kits

A wrap assembly for a urinary catheterization procedure, comprising:

• a foldable wrap body formed of a fabric, the foldable wrap body comprising:
• a first sterile component placement area;
• a second sterile component placement area positioned under the first sterile component placement area;
• a first folded edge along an upper border of the foldable wrap body in an unfolded configuration;
• and
• a second folded edge along a lower border of the foldable wrap body in the unfolded configuration, wherein the first folded edge and the second folded edge are creased inward toward a center of the foldable wrap body, and wherein the second folded edge includes an end of one side of the foldable wrap body separable from the second folded edge such that separation of the end of the one side of the foldable wrap body from over the first sterile component placement area reveals the second sterile component placement area;
• a first plurality of urinary catheterization components placed onto the fabric of the first sterile component placement area in a first order of use for the urinary catheterization procedure;
• and
• a second plurality of urinary catheterization components placed onto the fabric of the second sterile component placement area in a second order of use for the urinary catheterization procedure.