Thank you for writing.
It is possible to increase the size of the editor and the arrow button this way:
.radMultiColumnComboBox1.MultiColumnComboBoxElement.ArrowButtonMinWidth = 50;
As your application is targeting a touch device, I can also suggest using any of our Touch themes. These themes define greater sizes and fonts so that the controls would look better on a touch-enabled device: https://docs.telerik.com/devtools/winforms/styling-and-appearance/touch-themes
I hope this will help. Let me know if you need further assistance.
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