My organic textbook states the pathway for propyl tert-butyl ether in dilute sulfuric acid will follow E1 with a tertiary carbocation intermediate. It mentions that Sn1 will only occur with good nucleophiles.
It does not explain why however. Why is this any different than a tertiary haloalkane in water? I expect that the alcohol is a good leaving group, similar to water.
Vollhardt, P.; Schore, N. Molecules: Structure and Function, 7th edition; W. H. Freeman: New York, 2014, p350