What happens to the t-butyl cation in the TFA deprotection of a t-butyl ester? I am a first-year chemistry graduate student and I am currently learning how to synthesize proteins. I have reached a stage in the process where I need to deprotect a carboxylic acid moiety protected by t-butyl using trifluoroacetic acid (TFA).
I went online trying to find the mechanism for this step, but in terms of step-wise mechanism with electron movement arrows, the only thing I was able to find was this:


(Taken from here, no references therein)

While this looks legit, I am wondering about the t-butyl cation and its fate. 
My reaction is a bit simpler, and is presented below:


And my question is: is this truly where the deprotection ends? Does the t-butyl cation remains in solution as pictured? 

(I know that a t-butyl cation is considered to be relatively stable on account of it being a tertiary carbocation, but still I was not sure that it can remain in solution like that.)
The reaction is, in principle, catalytic in TFA. If t-butyltrifluoroacetate is the by-product, then the catalyst is consumed. If only isobutylene is formed, catalytic is OK. Using excess TFA covers all contingencies. In the initial step, protonation is more likely on the C=O oxygen. Higher electron density.