Will you clarify "adjacent"? And give an example of what you are attempting to accomplish.
A common "assignment of vector data sttributes from other data" is spatial overlay. The resultant product is the combination of 2 layers, for example, land use and soil type, to create a new layer, land use by soil type.
Another utilizies a buffer to assign the street name to the address portion of a land parcel. This is accomplished by buffering the street centreline by 10 meters (30 feet) - half the road allowance - then copying the street name to all land parcels that overlap the buffer. Note that this method may assign an incorrect street name to a parcel.
Hope this helps