Per the 2016 RNC Rules, here is the process for replacing a candidate:
2016 REPUBLICAN NATIONAL COMMITTEE RULES
RULE NO. 9
Filling Vacancies in Nominations
- The Republican National Committee is hereby authorized and empowered to fill any and all vacancies which may occur by reason of death, declination, or otherwise of the Republican candidate for President of the United States or the Republican candidate for Vice President of the United States, as nominated by the national convention, or the Republican National Committee may reconvene the national convention for the purpose of filling any such vacancies.
- In voting under this rule, the Republican National Committee members representing any state shall be entitled to cast the same number of votes as said state was entitled to cast at the national convention.
- In the event that the members of the Republican National Committee from any state shall not be in agreement in the casting of votes hereunder, the votes of such state shall be divided equally, including fractional votes, among the members of the Republican National Committee present or voting by proxy.
- No candidate shall be chosen to fill any such vacancy except upon receiving a majority of the votes entitled to be cast in the election.
RULE NO. 1
- The members of the Republican National Committee shall consist of one (1) national committeeman and one (1) national committeewoman from, and the chairman of the state Republican Party of, each state.
So, what this means is that the 150-member Committee (three from each state) can remove and replace a candidate for POTUS or VPOTUS either by themselves or via reconvening the Convention (which, logistically, won’t happen since the election is only one month away).
So, this 150-member committee can choose whomever they want as the replacement. If the Convention was reconvened, Cruz would’ve had the upper hand. With the power being in this smaller committee, who knows.
Need to do some legwork to determine who exactly are on that Committee and where their they each align as far as political leanings, sympathies, attachments, etc.