Are there any shapefiles available online of ZCTAs (Zip code tabulation area) by state? The US Census bureau has an excellent list of ZCTAs but they do not indicate which state each ZCTA is in. They have a set of files that describe relationships between ZCTA and other districts, but not states.
Here are current links to the Census FTP page for ZCTA shapefiles:
ZCTAs cross state boundaries just like ZIP codes do, so you should expect a many-to-many relationship when you intersect the two layers. Hope that this is not too late to be helpful!
Edit: you may want to look at this post about using the files to answer your original question (Determining which US zipcodes map to more than one state or more than one city?)
Zip Code Tabulation Areas (ZCTA) are a US Census product derived from the Zipcodes defined by the USPS which, as a federal entity, may cross state and other administrative boundaries. They are semi-fuzzy boundaries based on the logistical delivery of mail and are subject to changes between censuses.
Per the census mandate, census data must adhere to state boundaries, so that is "where they draw the line".
The following is partially speculation on my part, but I believe the state reference is intentionally omitted for reasons of non-coherence with other federal data authorities.
The ZCTA lookup tables you mention should be considered the official index to a FIPS code. As a practical matter, one could also do a spatial join to the containing state/county boundary to determine the state most census ZCTAs are within.
You can download 2010 ZCTAs for individual states here: https://www.census.gov/cgi-bin/geo/shapefiles/index.php?year=2010&layergroup=ZIP+Code+Tabulation+Areas